[(1+1/n)·(1+1/n)·……·(1+1/n)·1]^[1/(n+1)]<[(1+1/n)+(1+1/n)+……+(1+1/n)+1]/(n+1) =(n+2)/(n+1) =1+1/(n+1), 即(1+1/n)^[n/(n+1)]<1+1/(n+1) ∴(1+1/n)^n<[1+1/(n+1)]^(n+1).
