求极限lim→∞(1/1x2+1/2×3+…+1/n×﹙n+1﹚)

Question

求极限lim→∞(1/1x2+1/2×3+…+1/n×﹙n+1﹚)

Answer 1

1/1x2+1/2×3+…+1/n×﹙n+1）
=1-1/2+1/2-1/3+…+1/n-1/n+1
=1-1/n+1
=n/n+1
分子分母同时÷n 得1/(1+1/n)
极限为1