几种正项级数判别法的强弱比较

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1、几种正项级数判别法的强弱比较2008???h24?'SCIENCE&TECHNOLOGYINFORMATION???????????6???q?t?c?i?????y???x??????????????,?????????x???C???6???q?????????????6???q???????????q??.?????????????6???q?t?c?????????????????s?[???K?C??????????,?5???????????H???I???????J???????O?H???t?c????????????

2、f0??f2??????????mDn=1!rn(0<r<1)?z?I?????????t?a?t?c??????????1.D'Alembert?t?c???.?????G?t?c????mFun?z????????,?A"N0>0???x??q(0<q<1)(1)???????In>N0?Y???O???Gun+1unm?q,?1????????mFun?6??;(2)???????In>N0?Y???O???Gun+1unm?1?1????mFun????.2.Cauchy?t?c???.???

3、o?G?t?c????mFun?z????????,?A"N0>0?????x??l(1)???????In>N0?Y???O???Gunn&l<1,?1????????mFun?6??;(2)???????In>N0?Y???O???Gunn&1,?1????mFun????f0???C1:Cauchy?t?c???z??D'Alembert?t?c??,??????????????,?????+D'Alembert?t?c?????????????q,?1?????+Cauchy?t?c??????

4、??f0?????O?6f0??:???????L???T?O???G:limne?mDinfun+1unm?limne?mDinfunn)limne?mDsupunn&limne?mDsupun+1un?????????h???a???L?O???G,?????????????7?????Lf0??8?=limne?mDsupun+1un????8?=mD,?????????Lf0????8??N??,??8?>8?,???N??????N,????nm?N??,un+1unm?8?????????p>0,uN+k+1m

5、?8?uN+k(k=0,1,2,m?,p-1)???????O???G????????,?s???fuN+pm?8?puN,?.?S,uNm?uN8?-N8?n(nm?N)???iunn&uN8?-Nn&,limne?mDsupunn&>8??&?G???Y??f0???ilimne?mDsupunn&:?t??????mF2+(-1)n2n???????q??:?s??limne?mDu2mu2m-1=limne?mD322m122m-1=32,limne?mDu2m+1u2m=limne?mD

6、122m+1322m=16.?d?sD'Alembert?t?c?????????c?t?c?????????6??f0???i,limne?mDunn&=limne?mD=2+(-1)nn&2=12,?J?????????i?6????f0??f2??s?e?P?8??????mDn=1%1ns(s>1)?z?I?????????t?a?t?c??????????1.Raabe?t?c??.??mFun?z????????,??limne?mDsupn(1-un+1un)=p*,limne?mDinfn(1-un+1u

7、n)=p?1,??p>1??mFun?6??,??p*<1??,mFun????f02.?????t?c??.??mF?z????????,??limne?mDsupln(1un)lnn=q*,limne?mDinfln(1un)lnn=q,?1,??q>1??mFun?6??,??q*<1??,mFun????f0??:??q>1??,????8?0>0,??q>1+8?.0???i,???+???6??N,??n>N???Nln(1un)lnn>1+8?0f0????,??n>N

8、???Nun<1n1+8?0,???HmFun?6??,?H?C??????q*<1??,mFun????f0???C2:?????t?c???z??R