
Originally Posted by
jstephenson
Hi,
I'm doing some revision, and am asked to prove by induction:
$\displaystyle n^n > 2^{n+1} \text{ for all } n \geqslant 3$
The provided solution has the obvious base step (n = 3), the following hypothesis:
$\displaystyle \text{Let } n \geqslant 3 \text{ such that } n^n > 2^{n+1}$
and the following step:
$\displaystyle (n + 1)^{n+1} > n^n \cdot n >_{IH} 2^{n+1} \cdot n > 2^{n+2}$
Regrettably I can't see how the inductive step leads to prove the hypothesis, and so am wondering if someone would be kind enough to break it down for me?
Thanks in advance,
James