先证明一个一般性的命题：n^(n+1)>(n+1)^n(n≥3)证明：①n=3时,3^4>4^3,命题成立.②n=k时,命题成立,即：k^(k+1)>(k+1)^k.k^(k+1)/(k+1)^k>1.则(k+1)^(k+2)/(k+2)^(k+1)=((k+1)/(k+2))^(k+1)•(k+1)>(k/(k+1))^(...