下例命题中正确的是:(A)若limn→∞(an•bn)=a≠0,则limn→∞an≠0且limn→∞bn≠0(B)若limn→∞(an·bn)=0,则limn→∞an=0且limn→∞bn=0(C)若limn→∞(an-bn)=0,则limn→∞an=limn→∞bn(D)若无穷数例｛an｝的

Question

下例命题中正确的是:(A)若limn→∞(an•bn)=a≠0,则limn→∞an≠0且limn→∞bn≠0
(B)若limn→∞(an·bn)=0,则limn→∞an=0且limn→∞bn=0 (C)若limn→∞(an-bn)=0,则limn→∞an=limn→∞bn(D) 若无穷数例｛an｝的极限则limn→∞an=limn→∞an＋1

Answer 1

A)不对,例如an = 1/n^2,bn= n^2,乘积极限为1,an极限为0,bn没极限
B) 不对,例如bn=1,an=1/n,两个不同时为0
C) 不对,必须有前提是an和bn极限存在
D) 对