From 472f8662a2cc23d62364549c4e855ad3c65b690d Mon Sep 17 00:00:00 2001 From: Daniel Bulant Date: Tue, 1 Oct 2024 11:40:35 +0200 Subject: [PATCH] vault backup: 2024-10-01 11:40:35 --- .../obsidian-activity-history/data.json | 16 +- .../obsidian-spaced-repetition/data.json | 2 +- .../various-complements/histories.json | 2 +- notes/.obsidian/workspace.json | 40 +-- notes/cjl/Básně.md | 12 + notes/cjl/cjl.md | 1 + ...loupnost 2024-09-26 13.01.57.excalidraw.md | 331 ++++++++++++++++++ notes/data/data.md | 6 + notes/eko/Hospodarsky proces.md | 41 +++ notes/eko/Majetek.md | 7 + notes/eko/eko.md | 1 + notes/mat/Posloupnost.md | 109 ++++++ 12 files changed, 544 insertions(+), 24 deletions(-) create mode 100644 notes/cjl/Básně.md create mode 100644 notes/data/Posloupnost 2024-09-26 13.01.57.excalidraw.md create mode 100644 notes/eko/Majetek.md diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json index ca9ee2f..97b8dc7 100644 --- a/notes/.obsidian/plugins/obsidian-activity-history/data.json +++ b/notes/.obsidian/plugins/obsidian-activity-history/data.json @@ -12,8 +12,8 @@ "checkpointList": [ { "path": "/", - "date": "2024-09-24", - "size": 4982258 + "date": "2024-10-01", + "size": 4765369 } ], "activityHistory": [ @@ -1619,6 +1619,18 @@ { "date": "2024-09-24", "value": 4243 + }, + { + "date": "2024-09-25", + "value": 228419 + }, + { + "date": "2024-09-26", + "value": 9516 + }, + { + "date": "2024-10-01", + "value": 1634 } ] } diff --git a/notes/.obsidian/plugins/obsidian-spaced-repetition/data.json b/notes/.obsidian/plugins/obsidian-spaced-repetition/data.json index 21adb37..95b8ac2 100644 --- a/notes/.obsidian/plugins/obsidian-spaced-repetition/data.json +++ b/notes/.obsidian/plugins/obsidian-spaced-repetition/data.json @@ -38,7 +38,7 @@ "maxLinkFactor": 1, "showDebugMessages": false }, - "buryDate": "2024-09-25", + "buryDate": "2024-10-01", "buryList": [], "historyDeck": null } \ No newline at end of file diff --git a/notes/.obsidian/plugins/various-complements/histories.json b/notes/.obsidian/plugins/various-complements/histories.json index 5d247d7..6b1281d 100644 --- a/notes/.obsidian/plugins/various-complements/histories.json +++ b/notes/.obsidian/plugins/various-complements/histories.json @@ -1 +1 @@ -{"^{n+1}$":{"^{n+1}$":{"currentFile":{"count":1,"lastUpdated":1727163394804}}},"peníze":{"peníze":{"currentFile":{"count":1,"lastUpdated":1727169498404}}},"zboží":{"zboží":{"currentFile":{"count":1,"lastUpdated":1727169511752}}}} \ No newline at end of file +{"^{n+1}$":{"^{n+1}$":{"currentFile":{"count":1,"lastUpdated":1727163394804}}},"peníze":{"peníze":{"currentFile":{"count":1,"lastUpdated":1727169498404}}},"zboží":{"zboží":{"currentFile":{"count":1,"lastUpdated":1727169511752}}},"18-\\frac35$":{"18-\\frac35$":{"currentFile":{"count":1,"lastUpdated":1727350259680}}},"2-2+4$":{"2-2+4$":{"currentFile":{"count":1,"lastUpdated":1727351726507}}},"dřevo":{"dřevo":{"currentFile":{"count":1,"lastUpdated":1727773994843}}}} \ No newline at end of file diff --git a/notes/.obsidian/workspace.json b/notes/.obsidian/workspace.json index 83f2f9c..81ead76 100644 --- a/notes/.obsidian/workspace.json +++ b/notes/.obsidian/workspace.json @@ -4,28 +4,28 @@ "type": "split", "children": [ { - "id": "6fc77342ea8daf26", + "id": "f1b3353173ba94a0", "type": "tabs", "children": [ { - "id": "61fce6f2d25a77a3", + "id": "8f52afcb8e614f9e", "type": "leaf", "state": { "type": "markdown", "state": { - "file": "mat/Posloupnost.md", + "file": "eko/Marek.md", "mode": "source", "source": false } } }, { - "id": "1c0f7c6619f8de34", + "id": "7f98da99b4a75a53", "type": "leaf", "state": { "type": "markdown", "state": { - "file": "conflict-files-obsidian-git.md", + "file": "eko/Hospodarsky proces.md", "mode": "source", "source": false } @@ -61,7 +61,7 @@ "state": { "type": "search", "state": { - "query": "d=2b", + "query": "pohled", "matchingCase": false, "explainSearch": false, "collapseAll": true, @@ -98,7 +98,7 @@ "state": { "type": "backlink", "state": { - "file": "conflict-files-obsidian-git.md", + "file": "eko/Hospodarsky proces.md", "collapseAll": false, "extraContext": false, "sortOrder": "alphabetical", @@ -115,7 +115,7 @@ "state": { "type": "outgoing-link", "state": { - "file": "conflict-files-obsidian-git.md", + "file": "eko/Hospodarsky proces.md", "linksCollapsed": false, "unlinkedCollapsed": true } @@ -162,7 +162,7 @@ "state": { "type": "outline", "state": { - "file": "conflict-files-obsidian-git.md" + "file": "eko/Hospodarsky proces.md" } } }, @@ -227,11 +227,11 @@ } } ], - "currentTab": 11 + "currentTab": 3 } ], "direction": "horizontal", - "width": 300, + "width": 200, "collapsed": true }, "left-ribbon": { @@ -251,11 +251,17 @@ "breadcrumbs:Breadcrumbs Visualisation": false } }, - "active": "1c0f7c6619f8de34", + "active": "8c976bdcdc74c84c", "lastOpenFiles": [ - "mat/Posloupnost.md", - "conflict-files-obsidian-git.md", "eko/Marek.md", + "eko/Hospodarsky proces.md", + "eko/Majetek.md", + "eko/Podnikání.md", + "mat/mat.md", + "mat/Posloupnost.md", + "data/Posloupnost 2024-09-26 13.01.57.excalidraw.md", + "cjl/Básně.md", + "conflict-files-obsidian-git.md", "mat/Funkce/Funkce.md", "pva/skripta.md", "pva/vasek.md", @@ -268,18 +274,12 @@ "eko/eko.md", "mat/Geometrie/Analytická/Vektor.md", "mat/Geometrie/Analytická/Kuželosečky.md", - "mat/mat.md", - "eko/Podnikání.md", "eko/Pracovní proces.md", "fyz/elektrika/fotoveci.md", "export/export.md", "vyp/Cenová politika a swot analýza.md", "export/Buffer Overflow/Buffer Overflow.md", "data/Příklady 2024-03-15 11.06.56.excalidraw.svg", - "data/Příklady 2024-03-15 11.06.56.excalidraw.md", - "cjl/literatura/Tropy a figury.md", - "mat/Geometrie/Analytická/Hyperbola.md", - "mat/Geometrie/Analytická/Elipsa.md", "data/Parabola 2024-03-22 11.31.41.excalidraw.svg", "data/Parabola 2024-03-21 11.58.33.excalidraw.svg", "data/Parabola 2024-03-21 11.18.48.excalidraw.svg", diff --git a/notes/cjl/Básně.md b/notes/cjl/Básně.md new file mode 100644 index 0000000..db9e576 --- /dev/null +++ b/notes/cjl/Básně.md @@ -0,0 +1,12 @@ +# Básně + + +Podstatné jméno, přídavné jméno, sloveso + +pitomý člověk jezdí +modrá konzole spí +modrá voda vytváří +ujeté hodiny kopou + + +hučí starý papír \ No newline at end of file diff --git a/notes/cjl/cjl.md b/notes/cjl/cjl.md index b5095d2..49678ba 100644 --- a/notes/cjl/cjl.md +++ b/notes/cjl/cjl.md @@ -7,6 +7,7 @@ type: folder_brief_live imagePrefix: 'data/' ``` %% Zoottelkeeper: Beginning of the autogenerated index file list %% +- [[cjl/Básně|Básně]] - [[cjl/hodiny|hodiny]] - [[cjl/impresionismus atd|impresionismus atd]] - [[cjl/jazyky/jazyky|jazyky]] diff --git a/notes/data/Posloupnost 2024-09-26 13.01.57.excalidraw.md b/notes/data/Posloupnost 2024-09-26 13.01.57.excalidraw.md new file mode 100644 index 0000000..cdfb214 --- /dev/null +++ b/notes/data/Posloupnost 2024-09-26 13.01.57.excalidraw.md @@ -0,0 +1,331 @@ +--- + +excalidraw-plugin: parsed +tags: [excalidraw] + +--- +==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== + + +# Text Elements +sin n pi ^LuehYMRv + +1 pi = 3pi = 5pi ^4ML407yx + +2pi=4pi=6pi ^FEpFSx8H + +0 ^Y8Pq3auh + +%% +# Drawing +```json +{ + "type": "excalidraw", + "version": 2, + "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/1.9.27", + "elements": [ + { + "id": "4W9-4C_-tAeitn4-wbbWN", + "type": "ellipse", + "x": -466.3406066894531, + "y": -299.9718780517578, + "width": 487.199951171875, + "height": 474, + "angle": 0, + "strokeColor": "#1e1e1e", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "roundness": { + "type": 2 + }, + "seed": 345032185, + "version": 82, + "versionNonce": 1059390681, + "isDeleted": false, + "boundElements": null, + "updated": 1727348530806, + "link": null, + "locked": false + }, + { + "id": "5VGTnJtZ7yzy-CY2B5plf", + "type": "line", + "x": -553.9407653808594, + "y": -69.57191467285156, + "width": 622.7999877929688, + "height": 2.39996337890625, + "angle": 0, + "strokeColor": "#e03131", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "roundness": { + "type": 2 + }, + "seed": 1438712249, + "version": 113, + "versionNonce": 906861559, + "isDeleted": false, + "boundElements": null, + "updated": 1727348571654, + "link": null, + "locked": false, + "points": [ + [ + 0, + 0 + ], + [ + 622.7999877929688, + -2.39996337890625 + ] + ], + "lastCommittedPoint": null, + "startBinding": null, + "endBinding": null, + "startArrowhead": null, + "endArrowhead": null + }, + { + "id": "G0eV8wcj2bAtg_PYF9hTU", + "type": "line", + "x": -233.54067993164062, + "y": -453.57191467285156, + "width": 14.4000244140625, + "height": 740.4000854492188, + "angle": 0, + "strokeColor": "#1e1e1e", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "roundness": { + "type": 2 + }, + "seed": 1390571607, + "version": 96, + "versionNonce": 1329322713, + "isDeleted": false, + "boundElements": null, + "updated": 1727348539181, + "link": null, + "locked": false, + "points": [ + [ + 0, + 0 + ], + [ + 14.4000244140625, + 740.4000854492188 + ] + ], + "lastCommittedPoint": null, + "startBinding": null, + "endBinding": null, + "startArrowhead": null, + "endArrowhead": null + }, + { + "id": "LuehYMRv", + "type": "text", + "x": -103.94070434570312, + "y": -338.3719024658203, + "width": 68.159912109375, + "height": 25, + "angle": 0, + "strokeColor": "#1e1e1e", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "roundness": null, + "seed": 1144790103, + "version": 9, + "versionNonce": 941543321, + "isDeleted": false, + "boundElements": null, + "updated": 1727348542766, + "link": null, + "locked": false, + "text": "sin n pi", + "rawText": "sin n pi", + "fontSize": 20, + "fontFamily": 1, + "textAlign": "left", + "verticalAlign": "top", + "baseline": 17, + "containerId": null, + "originalText": "sin n pi", + "lineHeight": 1.25 + }, + { + "id": "4ML407yx", + "type": "text", + "x": -558.7406921386719, + "y": -89.97187805175781, + "width": 148.79977416992188, + "height": 25, + "angle": 0, + "strokeColor": "#1e1e1e", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "roundness": null, + "seed": 1897954649, + "version": 27, + "versionNonce": 815524343, + "isDeleted": false, + "boundElements": null, + "updated": 1727348560646, + "link": null, + "locked": false, + "text": "1 pi = 3pi = 5pi", + "rawText": "1 pi = 3pi = 5pi", + "fontSize": 20, + "fontFamily": 1, + "textAlign": "left", + "verticalAlign": "top", + "baseline": 17, + "containerId": null, + "originalText": "1 pi = 3pi = 5pi", + "lineHeight": 1.25 + }, + { + "id": "FEpFSx8H", + "type": "text", + "x": 31.659393310546875, + "y": -104.37190246582031, + "width": 107.23985290527344, + "height": 25, + "angle": 0, + "strokeColor": "#1e1e1e", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "roundness": null, + "seed": 2135234615, + "version": 12, + "versionNonce": 777924697, + "isDeleted": false, + "boundElements": null, + "updated": 1727348568309, + "link": null, + "locked": false, + "text": "2pi=4pi=6pi", + "rawText": "2pi=4pi=6pi", + "fontSize": 20, + "fontFamily": 1, + "textAlign": "left", + "verticalAlign": "top", + "baseline": 17, + "containerId": null, + "originalText": "2pi=4pi=6pi", + "lineHeight": 1.25 + }, + { + "id": "Y8Pq3auh", + "type": "text", + "x": -210.74063110351562, + "y": -104.37190246582031, + "width": 13.759994506835938, + "height": 25, + "angle": 0, + "strokeColor": "#e03131", + "backgroundColor": "transparent", + "fillStyle": "solid", + "strokeWidth": 2, + "strokeStyle": "solid", + "roughness": 1, + "opacity": 100, + "groupIds": [], + "frameId": null, + "roundness": null, + "seed": 982170585, + "version": 7, + "versionNonce": 1654559449, + "isDeleted": false, + "boundElements": null, + "updated": 1727348577936, + "link": null, + "locked": false, + "text": "0", + "rawText": "0", + "fontSize": 20, + "fontFamily": 1, + "textAlign": "left", + "verticalAlign": "top", + "baseline": 17, + "containerId": null, + "originalText": "0", + "lineHeight": 1.25 + } + ], + "appState": { + "theme": "dark", + "viewBackgroundColor": "#ffffff", + "currentItemStrokeColor": "#e03131", + "currentItemBackgroundColor": "transparent", + "currentItemFillStyle": "solid", + "currentItemStrokeWidth": 2, + "currentItemStrokeStyle": "solid", + "currentItemRoughness": 1, + "currentItemOpacity": 100, + "currentItemFontFamily": 1, + "currentItemFontSize": 20, + "currentItemTextAlign": "left", + "currentItemStartArrowhead": null, + "currentItemEndArrowhead": "arrow", + "scrollX": 1169.4656982421875, + "scrollY": 873.628173828125, + "zoom": { + "value": 1 + }, + "currentItemRoundness": "round", + "gridSize": null, + "gridColor": { + "Bold": "#C9C9C9FF", + "Regular": "#EDEDEDFF" + }, + "currentStrokeOptions": null, + "previousGridSize": null, + "frameRendering": { + "enabled": true, + "clip": true, + "name": true, + "outline": true + } + }, + "files": {} +} +``` +%% \ No newline at end of file diff --git a/notes/data/data.md b/notes/data/data.md index 5dc7b5d..cbfba79 100644 --- a/notes/data/data.md +++ b/notes/data/data.md @@ -49,6 +49,7 @@ imagePrefix: 'data/' - [[data/Hyperbola 2024-03-14 11.33.16.excalidraw|Hyperbola 2024-03-14 11.33.16.excalidraw]] - [[data/Kartézský součin_2022-01-19 09.25.49.excalidraw|Kartézský součin_2022-01-19 09.25.49.excalidraw]] - [[data/Kmitový pohyb 2023-04-25 12.31.10.excalidraw|Kmitový pohyb 2023-04-25 12.31.10.excalidraw]] +- [[data/Kombinace variace permutace 2024-06-07 11.12.16.excalidraw.svg|Kombinace variace permutace 2024-06-07 11.12.16.excalidraw.svg]] - [[data/Kombinace variace permutace 2024-06-07 11.12.16.excalidraw|Kombinace variace permutace 2024-06-07 11.12.16.excalidraw]] - [[data/Konstrukční úlohy 2023-09-08 11.27.10.excalidraw|Konstrukční úlohy 2023-09-08 11.27.10.excalidraw]] - [[data/Konstrukční úlohy 2023-09-08 11.36.28.excalidraw|Konstrukční úlohy 2023-09-08 11.36.28.excalidraw]] @@ -448,6 +449,11 @@ imagePrefix: 'data/' - [[data/Pasted image 20240301122558.png|Pasted image 20240301122558.png]] - [[data/Pasted image 20240607110822.png|Pasted image 20240607110822.png]] - [[data/Pasted image 20240607110825.png|Pasted image 20240607110825.png]] +- [[data/Pasted Image 20240607111318_511.png|Pasted Image 20240607111318_511.png]] +- [[data/Pasted Image 20240607113016_141.png|Pasted Image 20240607113016_141.png]] +- [[data/Pasted Image 20240607120859_000.png|Pasted Image 20240607120859_000.png]] +- [[data/Pasted Image 20240607123213_059.png|Pasted Image 20240607123213_059.png]] +- [[data/Posloupnost 2024-09-26 13.01.57.excalidraw|Posloupnost 2024-09-26 13.01.57.excalidraw]] - [[data/Posunutí o vektor 2023-12-15 11.33.14.excalidraw|Posunutí o vektor 2023-12-15 11.33.14.excalidraw]] - [[data/Pravidelný n-úhelník 2023-10-13 12.07.37.excalidraw|Pravidelný n-úhelník 2023-10-13 12.07.37.excalidraw]] - [[data/Priklady 2023-12-14 13.52.36.excalidraw|Priklady 2023-12-14 13.52.36.excalidraw]] diff --git a/notes/eko/Hospodarsky proces.md b/notes/eko/Hospodarsky proces.md index 4168d9a..7b256ed 100644 --- a/notes/eko/Hospodarsky proces.md +++ b/notes/eko/Hospodarsky proces.md @@ -1,6 +1,11 @@ # Hospodarsky proces +zisk = příjmy - výdaje +Ze zisku jsou daně + +Výdaje jsou mzdy, energie atd +Patří do nich ale i část dlouhodobého hmotného investičního majetku ## Kolobeh @@ -8,6 +13,42 @@ pro cizy spotrebu +Majetek +- materiál + - oběžný majetek + - může být též zboží + - prostředek jednorázové spotřeby + - materiál je např. dřevený trám, surovina je strom/dřevo + - může být výrobek jiné firmy +- polotovar + - součástky, hotové produkty které se kompletují +- Dlouhodobý hmotný investiční majetek + - Doba >1rok + - pořizovací cena >80k kč + - třeba auto, část z nich se počítá do výdajů, proto jsou podmínky a je to rozdělený +- Drobný hmotný investiční majetek + - Doba <1rok, **nebo** + - pořizovací cena <80k kč +- Nehmotný investiční majetek + - cena neurčena + - doba >1rok + - software, licence, patenty, receptury, značka, autorská práva, etc +- Finanční investiční majetek + - cena neurčena + - doba >1rok + - spořící účet, dluhopisy, cenné papíry, akcie, podílové listy, sbírkové předměty, drahé kovy, etc + - Umělecká galerie co pak prodá obrazy je nemá v FIM ale jako zboží/oběžný majetek + +Členění dlouhodobého majetku je navázáno na daňové zákony, zejména evidence daní z příjmu. + +Do nedokončené výroby jsme dali investici a proto se eviduje. + +- zboží +- pohledávka + - dodavatel za odběratelem + - zboží bylo dodáno ale nebylo zaplaceno + - nebo naopak odběratel za dodavatelem, pří záloze ale nebyla dodána + ### Rozdeleni distribuce ### Smeny diff --git a/notes/eko/Majetek.md b/notes/eko/Majetek.md new file mode 100644 index 0000000..8e248cf --- /dev/null +++ b/notes/eko/Majetek.md @@ -0,0 +1,7 @@ +# Majetek +Účetnictví, jestliže je v pronájmu nebo ho vlastní firma + +- oběžný majetek + - materiál + - on se přetvoří v produkt + - prostředek jednorázové spotřeby diff --git a/notes/eko/eko.md b/notes/eko/eko.md index 4fe286f..c062c84 100644 --- a/notes/eko/eko.md +++ b/notes/eko/eko.md @@ -1,6 +1,7 @@ # eko %% Zoottelkeeper: Beginning of the autogenerated index file list %% - [[eko/Hospodarsky proces|Hospodarsky proces]] +- [[eko/Majetek|Majetek]] - [[eko/Marek|Marek]] - [[eko/Podnikání|Podnikání]] - [[eko/Pracovní proces|Pracovní proces]] diff --git a/notes/mat/Posloupnost.md b/notes/mat/Posloupnost.md index c04006f..3f54cb8 100644 --- a/notes/mat/Posloupnost.md +++ b/notes/mat/Posloupnost.md @@ -1,6 +1,15 @@ # Posloupnost Posloupnost je funkce $f$ s $Df=\mathbb{N}$ +Je omezená tehdy když je omezená shora i zdola + +Je omezená zdola $\Leftrightarrow\exists d\in\mathbb{R}:a_n\ge d\forall n\in\mathbb{N}$ +Je omezená shora $\Leftrightarrow \exists h \in\mathbb{R}:a_n\le h\forall n\in\mathbb{N}$ + +Klesající posloupnost je omezená shora jelikož je v $\mathbb{N} \Rightarrow$ začíná na 0 (pro $a_n=n$) a jen klesá + + + ## Zadání - vzorcem pro n-tý člen $a_n=2n+3$ @@ -143,6 +152,106 @@ $a_3=-3$ Není monotóní - sporem jsme dokázali neplatnost podmínek pro monotónost +--- + +Je monotónní posloupnost? + +$\{\sin n\pi\}_1^\infty$ + +Je konstantní +$\sin n\pi=0\forall n\in\mathbb{N}$ + +![[Posloupnost 2024-09-26 13.01.57.excalidraw]] + +Je omezená + +--- + +$\{\frac{2n+3}{3n+1}\}_1^\infty$ + +$\frac{2n+3}{3n+1}-\frac{2(n+1)+3}{3(n+1)+1}\lessgtr0$ + +$\frac{2n+3}{3n+1}-\frac{2n+2+3}{3n+3+1}\lessgtr0$ + +$\frac{2n+3}{3n+1}-\frac{2n+5}{3n+4}\lessgtr0$ + +$\frac{(2n+3)(3n+4)}{(3n+1)(3n+4)}-\frac{(2n+5)(3n+1)}{(3n+4)(3n+1)}\lessgtr0$ + +$\frac{6n^2+9n+8n+12}{9n^2+3n+12n}-\frac{6n^2+15n+2n+5}{9n^2+3n+12n}\lessgtr0$ + +$\frac{7}{9n^2+15n}\lessgtr0$ + +dole je kladné $\frac++$ + +$7>0$ + +je klesající $a_n>a_{n+1}$ +je omezená shora + +je omezená zdola, bude vždy kladné $2n+3>0;3n+1>0\Rightarrow + a +$ + +--- + +$a_n=\frac{3n}5-a_{n+1}+2a_{n+2};a_2=3;a_4=7$ + +$a_2=\frac{3*2}5-a_3+2a_4$ +$3=\frac65-a_3+2*7$ +$a_3=\frac65+14-3$ +$a_3=\frac65+11$ +$a_3=\frac15+12$ + +$a_1=\frac{3n}5-a_2+2*a_3$ +$a_1=\frac{3n}5-3+2*(\frac15+12)$ +$a_1=\frac35-3+\frac25+24$ +$a_1=22$ + +$a_3=\frac{3n}5-a_4+2a_5$ +$\frac15+12=\frac95-7+2a_5$ +$2a_5=\frac15+12-\frac95+7$ +$2a_5=19-\frac85$ +$2a_5=18-\frac35$ +$a_5=9-\frac3{10}$ +$a_5=8+\frac7{10}$ + +$a_{n+2}=a_n-n+4;a_3=1;a_2=2$ + +$a_3=a_1-1+4$ +$1=a_1-1+4$ +$a_1=-2$ + +$a_4=a_2-2+4$ +$a_4=2-2+4$ +$a_4=4$ + +$a_5=a_3-3+4$ +$a_5=1-3+4$ +$a_5=2$ + + +--- + +Přepis na rekurentní + +$\{\frac{2n-1}3\}^\infty_1$ + +$a_n-a_{n+1}=\frac{2n-1}3-\frac{2(n+1)-1}3$ +$a_n-a_{n+1}=\frac{2n-1}3-\frac{2n+1}3$ +$a_n-a_{n+1}=\frac{2n-1-2n-1}3=-\frac{2}3$ + +$a_{n+1}=a_n+\frac23$ + + +--- + +Je omezená? + +$\{2^n\}^\infty_1$ + +je roustoucí +=> je omezená zdola + +$2^{n+1}-2^n=2*2^n-2^n=2^n>0$ + ## Funkce ### Vlastnosti #### Monotónost