lim n→无穷 (n+1/n-1)^n求极限

2个回答

(n+1/n-1)^n=(1+2/(n-1))^n,令u=2/(n-1). (1+2/(n-1))^n=(1+u)^[(1/u)un],因为(1+u)^(1/u)的极限为e,un=2n/(n-1)的极限为2,所以原极限为e^2.

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