關(guān)于無窮級(jí)數(shù)求和問題的探討畢業(yè)論文

1、1關(guān)于無窮級(jí)數(shù)求和問題的探討方先鋒（莆田學(xué)院數(shù)學(xué)系指導(dǎo)教師：林美琳）摘要：摘要：無窮級(jí)數(shù)是數(shù)學(xué)分析中的一個(gè)重要內(nèi)容無窮級(jí)數(shù)的和對(duì)于研究無窮級(jí)數(shù)的特性、函數(shù)斂散性、近似計(jì)算等都有重要的作用，本文介紹了無窮級(jí)數(shù)求和的一些方法，如裂項(xiàng)相消法、逐項(xiàng)微分或積分法、轉(zhuǎn)化為函數(shù)項(xiàng)級(jí)數(shù)求解法、利用子列的極限等等，以及這些方法在具體例子中的應(yīng)用，其目的是為了讓讀者更加熟練地掌握無窮級(jí)數(shù)求和方法及技巧，從而進(jìn)一步促進(jìn)其對(duì)該知識(shí)的學(xué)習(xí)和理解無窮級(jí)數(shù)，為以后更

2、深入的學(xué)習(xí)數(shù)學(xué)做好準(zhǔn)備。關(guān)鍵字：關(guān)鍵字：級(jí)數(shù)求和逐項(xiàng)積分函數(shù)項(xiàng)級(jí)數(shù)拉普拉斯變換Abstract:Infiniteseriesisanimptantpartofmathematicalanalysisinfiniteseriesfresearchtheacteristicsfunctioninfiniteseriesconvergesscatteredsexapproximatecomputationhasimptanteffectthi

3、spaperintroducessomemethodsofinfiniteseriessummationsuchasCancellationMethodofSplittingitembyitemaphotographofdifferentialintegralmethodistransfmedintoafunctionofseriesmethodusingsubsequencelimitetcthesemethodsinspecific

4、examplesofapplicationItspurposeistoletthereadermemasteredtheinfiniteseriessummationmethodsskillsthusfurtherpromoteitstotheknowledgelearningunderstinginfiniteseriesffurtherstudymathematicsready.Keywds:SeriessummationItemb

5、yitemintegralFunctionofseriesLaplacetransfm3231123...33333nnnS???????2由得：????12?21121111...333333nnnnnnSSS?????????即1112313113323313nnnnnnnS????????????????????于是2313limlim132332nnnnnnS????????????????????339lim224nnS???

6、???11934nnn??????2裂項(xiàng)相消法求和法裂項(xiàng)相消法求和法主要適用于無窮級(jí)數(shù)的通項(xiàng)公式為分式且其分母是因式之積的形式的級(jí)數(shù)。它的關(guān)鍵是將級(jí)數(shù)的一般項(xiàng)分解成部分分式的形式。諸如：，等等，??????11123nnnn????????22211nnn???都可以用裂項(xiàng)相消法求和。例3求無窮級(jí)數(shù)的和.????1112nnnn?????分析：觀察到此無窮級(jí)數(shù)的通項(xiàng)公式為分式且其分母是因式之積的形式的級(jí)數(shù)，注意到，然后再求和。?????

7、?????1111122112nnnnnnn?????????????解：因?yàn)??????????1111122112nunnnnnnn????????????????????1111111...212232334112nSnnnn??????????????????????????????????????????????11121212nn???????????所以????1111limlim212124nnnSnn?????????