正项级数的收敛与发散之间是不存在严格界限的

[]2000-06-01[](1964-),,,,(,124010)[],,[];;[]O17[]A[]10032191X(2000)0520049202n=1an(1)n=1bn(2)an+1an(1),1:(1)(2),n,an+1anbn+1bn,(1)(2)(2)(1)2:(1)(2),n,an+1anbn+1bn,(1)(2)(2)(1)(1)(2)1,(1),n=1Cn,n=1Cnan,(1):SK=n=1an(K)K=1SK+1-SKSK+1n=1Sn,PmN,vnNSn+12Sm;n=1Sn,K=mSK+1-SKSK+1SK+1-SKSn+1=Sn+1-SmSn+1=Sn+1-12Sn+1Sn+1=12,PmN,vnNK=mSK+1-SKSK+112,K=1SK+1-SKSK+1,K=1aK+1SK+1(SK+1-SK=aK+1)Ck=1SKK=1aKSK=K=1CKaKCn+1an+1Cnan=SnSn+1an+1anam+1an(Sn+1Sn)n=1Cnan(1)17520009JournalofLiaoningEducationalInstituteVol.17No.5Sep20002,(1),n=1Cnn=1Cnan,(1):rn=K=naK()anrn2(rn-rn+1)(3)rn+rn+12rnrn+1,-rn-rn+1-2rnrn+1rn-rn+12rn-2rnrn+1=2rn(rn-rn+1)an=rn-rn+1,an=2rn(rn-rn+1)anrn2(rn-rn+1)(3)n=1anrnn=12(rn-rn+1)=2(r1-limnrn)=2(r1-0)=2r1=2n=1an((1)limnrn=0)n=1anrnCn=1rn,n=1CnanCn+1an+1Cnan=rnrn+1an+1anan+1an(rnrn+1)k=nCnan(1)1;2:,n=1en,:n=1en,,,2,n=1Cnn=1Cnenn=1en,,,n=1en,,,[][1].[M].:,1992.0520005