在已知lim(1+1/n)^n=e的时候 求极限 lim(1+1/(n+1))^n-1=?
问题描述：
在已知lim(1+1/n)^n=e的时候 求极限 lim(1+1/(n+1))^n-1=?
答
令 m = n+1
(1+1/(n+1)) ^ (n-1) = (1+1/m) ^ (m-2) = [ (1+1/m) ^ m ] ^ { (m-2)/m }
(1+1/m) ^ m -> e,(m-2)/m -> 1
lim (1+1/(n+1)) ^(n-1) = e^1 = e