無(wú)窮級(jí)數(shù)習(xí)題及答案

1、1第十一章第十一章無(wú)窮級(jí)數(shù)無(wú)窮級(jí)數(shù)(A)用定義判斷下列級(jí)數(shù)的斂散性用定義判斷下列級(jí)數(shù)的斂散性1；2；3。????????112nnn??????12221nnn??????????15131nnn?判斷下列正項(xiàng)級(jí)數(shù)的斂散性判斷下列正項(xiàng)級(jí)數(shù)的斂散性4；5；6；7；8；???1100!nnn???1nneen????121nnn???????1332nnnn???14!nnn9；10。nnnn??????????113???????121n

2、nnn求下列任意項(xiàng)級(jí)數(shù)的斂散性，收斂時(shí)要說(shuō)明條件收斂或絕對(duì)收斂求下列任意項(xiàng)級(jí)數(shù)的斂散性，收斂時(shí)要說(shuō)明條件收斂或絕對(duì)收斂11；12；13????????11121nnnn??????2ln11nnn?????0001.1001.101.11.1；14；????????14413312221222求下列冪級(jí)數(shù)的收斂半徑和收斂區(qū)間求下列冪級(jí)數(shù)的收斂半徑和收斂區(qū)間15；16；17；18；???13nnnxn??????11nnnnnx???1!

3、nnxn??????1121nnnxn19；20；?????112121nnnx???123nnnxn求下列級(jí)數(shù)的和函數(shù)求下列級(jí)數(shù)的和函數(shù)21；22；????11nnnx121121?????nnnx將下列函數(shù)展開(kāi)成將下列函數(shù)展開(kāi)成的冪的級(jí)數(shù)的冪的級(jí)數(shù)0xx?23，；24，；2xxeeshx??00?xx2cos00?x25，；26，；????xx??1ln100?xx130?x將下列函數(shù)在區(qū)間將下列函數(shù)在區(qū)間上展開(kāi)為付里葉級(jí)數(shù)上展開(kāi)為

4、付里葉級(jí)數(shù)?????27，。28，??2cosxxA????????x??txf2?????????x317；18；19；???12nnnxnnxnn21!12???????12nnxn20求證：；?????1212lnnnn將下列函數(shù)展開(kāi)成將下列函數(shù)展開(kāi)成的冪的級(jí)數(shù)的冪的級(jí)數(shù)0xx?21，；22，；23，??13212???xxxf00?x??21xxf?10?x21xx?；00?x24證明偶函數(shù)的付里葉級(jí)數(shù)數(shù)僅含余弦項(xiàng)；25寫(xiě)出函數(shù)

5、，，的?????kxxf221??????????1212???kkx?210???k付里葉級(jí)數(shù)，并討論收斂情況。26設(shè)是周期為的周期函數(shù)，它在上的表達(dá)式為??xf?2?????，將展開(kāi)成付里葉級(jí)數(shù)。??????????????????????????????xxxxxf222222??xf27將函數(shù)，()分別展開(kāi)成正弦級(jí)數(shù)和余弦級(jí)數(shù)。??2xxf?lx??0(C)1用定義判斷下列級(jí)數(shù)的斂散性????????????13212121nn