Proving Inequalities with exponents by means of MI.

• Feb 14th 2013, 05:33 PM
Kaloda
Proving 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 PM
Plato
Re: Proving Inequalities with exponents by means of MI.
Quote:

Originally Posted by Kaloda
Using mathematical induction, prove that for all integers\$\displaystyle n\geq3\$,
\$\displaystyle (n+1)^n<n^{n+1}\$.

What is the first step in this proof? You can at least do that.
• Feb 15th 2013, 09:15 AM
Kaloda
Re: Proving Inequalities with exponents by means of MI.
Quote:

Originally Posted by Plato
What is the first step in this proof? You can at least do that.

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}\$.