Using mathematical induction, prove that for all integers$\displaystyle n\geq3$,
$\displaystyle (n+1)^n<n^{n+1}$.
Haha. Of course I do. I'm good in proving equality statements, i.e. sequence and summations,
using mathematical induction but not inequalities like this one.
What I did was I assumed that $\displaystyle k^{k-1}<(k-1)^k$ and then I tried to prove $\displaystyle (k+1)^k<k^{k+1}$.
After that, I really have no idea what to do next. Please help. TY.