n^(n+1/n)/(n+1/n)^n

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n^(n+1/n)/(n+1/n)^n
n^(n+1/n)/(n+1/n)^n

n^(n+1/n)/(n+1/n)^n
∑n^(n+1/n)/(n+1/n)^n
lima = limn^(n+1/n)/(n+1/n)^n
= limn^n*n^(1/n)/[n^n*(1+1/n^2)^n]
= limn^(1/n)/(1+1/n^2)^n
= limn^(1/n)/[(1+1/n^2)^n^2]^(1/n)
=l imn^(1/n)/e^(1/n) =1 .
故该级数发散.

n^(n+1/n)/(n+1/n)^n 2^n/n*(n+1) (n+1)^n-(n-1)^n=? 化简：(n+1)!/n!-n!/(n-1)! (n-1)*n!+(n-1)!*n 推导 n*n!=(n+1)!-n! 证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n n n n n 根号（n+1)+n n.(n-1). (n+2)!/(n+1)! 判断当n>1时,n*n*n>3n.( ) [3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简 [3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简 9题 = 101 (n+1)!- = n*n!n(n+1)!- n*n!