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
请详述过程.

Answer 1

A错,例如an=n,bn=1/n
B错,例如an=1,bn=1/n
C错,例如an=bn=n
D正确