绝对高手来 证明(1/n)^n+(2/n)^n+……+((n-1)/n)^n+(n/n)^n<e/(e-1) ....

首先困顷(1+1/磨扮x)^(x+1)>e（单调减极限是e）即e*x^(x+1)<(x+1)^(x+1)
下用数学归纳法证明
如果命题对n成立（原式等价于1^n+2^n+…+n^n则1^(n+1)+2^(n+1)+…瞎尺灶+n^(n+1)+(n+1)^(n+1)
<=n*(1^n+2^n+…+n^n)+(n+1)^(n+1)
<=n*e/(e-1)*n^n+(n+1)^(n+1)
<=e/(e-1)*n^(n+1)+(n+1)^(n+1)
<=1/(e-1)*(n+1)^(n+1)+(n+1)^(n+1)
=e/(e-1)*(n+1)^(n+1)