Using mathematical induction, prove that for all integers$\displaystyle n\geq3$,

$\displaystyle (n+1)^n<n^{n+1}$.

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- Feb 14th 2013, 05:33 PMKalodaProving Inequalities with exponents by means of MI.
Using mathematical induction, prove that for all integers$\displaystyle n\geq3$,

$\displaystyle (n+1)^n<n^{n+1}$. - Feb 14th 2013, 05:55 PMPlatoRe: Proving Inequalities with exponents by means of MI.
- Feb 15th 2013, 09:15 AMKalodaRe: Proving Inequalities with exponents by means of MI.
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.