Question

当n趋于∞,[(n+1)^(n+1)/n^n]sin(1/n)的极限怎么求

Answer 1

[(n+1)^(n+1)/n^n ] sin(1/n)

=(n+1) [1+1/n]^n sin(1/n)

[1+1/n]^n e

sin(1/n) 1/n

带入以后得到

=(n+1) [1+1/n]^n sin(1/n)

= (n+1) * 1/n * e = e