用数学归纳法证明:当n>=3时,n^n+1>(n+1)^n

n=3
3^(3+1)=3^4=81
(3+1)^3=4^3=64
3^(3+1)>(3+1)^3成立
设n=k k^(k+1)> 成立
k*k^k>(k+1)^k
k>[(k+1)/k]^k
=(1+1/k)^k
>[1+1/(k+1)]^k
k>[1+1/(k+1)]^k
k>[(k+2)/(k+1)]^k
k(k+1)^k>(k+2)^k
k^2(k+1)^k>k(k+2)^k
(k+1)^(k+2)>(k+2)^(k+1)
(k+1)^[(k+1)+1]>[(k+1)+1]^(k+1)
n=k+1 时成立
n^n+1>(n+1)^n得证