數(shù)學(xué)畢業(yè)論文-新探級數(shù)收斂的判別方法

新探級數(shù)收斂的判別方法

摘 要

本論文給出了級數(shù)收斂判別的幾種新方法.（1）隔項(xiàng)比值判別法:它較比式判別法更精細(xì).用比式判別方法可以判別的級數(shù),用隔項(xiàng)比值判別法可以判別,用隔項(xiàng)比值判別法可以判別的級數(shù),卻不1定能用比式判別法判別,即隔項(xiàng)比值判別法應(yīng)用更廣泛,但也更復(fù)雜些;（2）以調(diào)和級數(shù)為比較對象的比較判別法:在 級數(shù)中,當(dāng) 時(shí),級數(shù)收斂,當(dāng)
時(shí),級數(shù)發(fā)散,當(dāng) =1時(shí),即為調(diào)和級數(shù),它為收斂與發(fā)散的分界點(diǎn);（3）阿貝爾判別法的推廣:阿貝爾判別法中,改變它的條件,得到新的判別方法;（4）函數(shù)判別法:該判別方法的包容性很強(qiáng),只要適當(dāng)?shù)倪x取滿足條件的函數(shù),則可以得到1些具體的判別方法,即該方法為1些具體方法的普遍公式.
關(guān)鍵詞:級數(shù); 收斂; 發(fā)散; 判別法

Probe the Criterion of the Convergence for Series Newly

ABSTRACT

This paper has introduced several new criterions for the convergence of series. The first one is gap ratio criterion: It compares the ratio criterion to be finer. The gap ratio criterion can differentiate all the series that can be differentiated by the ratio criterion , but the series that can be differentiated by the gap ratio criterion, not necessarily can use the ratio actually to differentiate, namely the gap ratio criterion is much more widely used, but more complicated. The second one is comparison criterion which take harmonic series as the comparison object: When , the  -series converges, When , the  -series diverges. When, the  -series names harmonic series .it is the dividing line of convergence and divergence. The third criterion is the promotion of Abel criterion: If we change the conditions of the Abel criterion, we will obtain some new criterions. The fourth criterion is function criterion: the capacity of this criterion is very strong, so long as we select the suitable functions that satisfy its conditions, we will obtain some concrete criterions. This criterion is a universal formula.
Key words: series; convergence; divergence; criterion

目 錄

中文標(biāo)題-----------------------------------------------------------------------1
中文摘要、關(guān)鍵詞---------------------------------------------------------------1
英文標(biāo)題-----------------------------------------------------------------------1
英文摘要、關(guān)鍵詞----------------------------------------------------------------2
前言---------------------------------------------------------------------------3
正文---------------------------------------------------------------------------4
1 基本概念和定理----------------------------------------------------------------4
2 隔項(xiàng)比值判別法----------------------------------------------------------------5
3 以調(diào)和級數(shù)為比較對象的比較判別法-----------------------------------------------11
4 阿貝爾判別法的推廣------------------------------------------------------------13
5 函數(shù)判別法-------------------------------------------------------------------16
6 結(jié)束語-----------------------------------------------------------------------18
參考文獻(xiàn)-----------------------------------------------------------------------20
致謝---------------------------------------------------------------------------21

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