正項(xiàng)級(jí)數(shù)收斂性判別法的推廣-數(shù)學(xué)專業(yè)本科畢業(yè)論文

1、正項(xiàng)級(jí)數(shù)收斂性判別法的推廣正項(xiàng)級(jí)數(shù)收斂性判別法的推廣摘要：正項(xiàng)級(jí)數(shù)收斂的判別法在級(jí)數(shù)的收斂法中占有極其重要的地位常見(jiàn)的判別法有比較判別法，達(dá)朗貝爾比值判別法，柯西判別法，高斯判別法柯西積分判別法等對(duì)于上述判別法，它們都有一定的條件限制，為了找到更簡(jiǎn)單，適用條件更廣的判別法，國(guó)內(nèi)外學(xué)者或者在一般判別法的基礎(chǔ)上做了推廣或者提出了一些新的判別法近幾年，關(guān)于正項(xiàng)級(jí)數(shù)收斂性判別法又有了一些新的研究，主要是針對(duì)一些新判別法的適用條件進(jìn)行了討論本文主

2、要分兩部分對(duì)正項(xiàng)級(jí)數(shù)的判別法進(jìn)行了推廣，第一部分對(duì)比值判別法進(jìn)行了推廣，給出了比值判別法在失效情況下的判別方法，這也是本文的主要部分，第二部分對(duì)比較判別法進(jìn)行了推廣這些推廣的新的判別法解決了原判別法的條件限制，使其更具一般性，適用性更廣關(guān)鍵詞關(guān)鍵詞：正項(xiàng)級(jí)數(shù)；收斂性；發(fā)散性；判別法AGeneralizationofConvergenceCriterionfPositiveProgressionsYangRui(0301Mathemati

3、csAppliedMathematicsSchoolofScience)Theinstruct:SongWenqingAbstract:ConvergenceCriterionfPositiveProgressionsholdstheextremelyimptantstatusintheprogressionThecommoncriterionsincludethecomparisondistinctionlawreachesthebr

4、ightBellratiodistinctionlawwestthetanoakdistinguishesthelawGaussdistinguishesthelawwestthetanoaktheintegraldistinctionlawsoonbutthesedistinctionlawsallhavethecertainconditionlimitIndertofindoutmesimplymewidelyuseddistinc

5、tionlawsdomesticfeignscholarshavemadesomepromotionwkedoutsomenewdistinctionlawsInrecentyearsthereareseveralnewresearchesaboutpositiveprogressionsastringencydistinguishedthelawmainlyaimingatdiscussingapplicablerequirement

6、sofnewdistinctionlawThisarticlewasmainlydividedin2partstocarryonthepromotionoftheseriesofpositiveprogressionsdistinctionlawThefirstpartpromotesspecificvaluedistinctionlawaswellasshowsdistinguishablemethodswhenitdoesn’twk

7、ItisalsothemainpartofthiswkThesecondpartcarriesonthepromotionofthecomparisondistinctionlawitusesthecrespondingdistinctionlawtojudgetheseriesofpositiveprogressionsastringencyThesenewdistinctionlawshavesolvedtherequirement

8、allimitsoftheiginaldistinctionlawsmakingthemmegeneralmakingtheirserviceabilitybroaderKeywds:positiveprogressionseriesconvergencedivergencecriterion21達(dá)朗貝爾判別法的一類推廣與應(yīng)用由達(dá)朗貝爾判別法判別法極限形式知，當(dāng)時(shí)，正項(xiàng)級(jí)數(shù)可能收斂也1lim1nnnuu????nu?可能發(fā)散，我們無(wú)法直

9、接用達(dá)朗貝爾判別法判別法判斷其斂散性，此時(shí)這種判別法失效，為了解決這一問(wèn)題，給出新的判別法新的判別法適用條件更廣，運(yùn)算更簡(jiǎn)潔211達(dá)朗貝爾判別法判別法的第一種推廣引理正項(xiàng)級(jí)數(shù)若，且則??211nna???10nnaa?????12n??2limnnnnapa???(i)當(dāng)p時(shí)，則級(jí)數(shù)發(fā)散121nna???定理1若，則級(jí)數(shù)收斂當(dāng)且僅當(dāng)收斂（其中??710nnaa?????12n??1nna???1nnmnma???m是大于1的正整數(shù)）證明