I need a hint on a proof using mathematical induction I'm trying to prove that $k^k+1\ge2^k$ using mathematical induction but i'm missing something. How can i establish the binomial $(k+1)^{k+1}$? As a first step, i multiplied both sides by $2$ and $k$ but i can't get further than this without distorting things. Can someone give me a hint? Thanks in advance.

Why bother use mathematical induction? For $k\ge2$, we have $k^k+1\ge2^k+1>2^k$.  

Maybe prove $k^k\ge2^k$ ($k\ge2$) would be much easier. Since $$(k+1)^{k+1}>(k+1)k^k\ge(k+1)2^k>2^{k+1},$$ mathematical induction can easily be applied.
