Question

求lim n→∞ ((√n+1)-√n)

过程

Answer 1

lim n→∞ ((√n+1)-√n)
=lim n→∞ ((√n+1)-√n)((√n+1)+√n) / ((√n+1)+√n)
=lim n→∞ 1 / ((√n+1)+√n)
=lim n→∞ 1/√n / ((√1+1/n)+√1)...........f分子分母同时除以√n
=lim n→∞ 1/√n
=0

Answer 2

lim n→∞ ((√n+1)-√n)
=lim n→∞ [1/(√n+1)+√n)]
=0

Answer 3

(√n+1)-√n
=[(√n+1)-√n][(√n+1)+√n]/[(√n+1)+√n]
=(n+1-n)/[(√n+1)+√n]
=1/[(√n+1)+√n]

所以极限=0