The Basis is easy, my algebra sucks, can someone please help me with the inductive step? Even just a nice hint or start would be great.
Thanks in advance.
so your base case is for n = 2.
you want to show P(2) holds.
then assume P(n) holds for some n
then use that to show P(n + 1) holds.
to start you off.
Let $\displaystyle P(n)$: "$\displaystyle 3^n + 4^n \le 5^n$ for all $\displaystyle n \in \mathbb{N},~n \ge 2$"
So, $\displaystyle P(2)$: $\displaystyle 3^2 + 4^2 = 9 + 16 = 25 \le 5^2$
so, $\displaystyle P(2)$ holds.
Assume $\displaystyle P(n)$ holds for some $\displaystyle n \ge 2$, we show $\displaystyle P(n + 1)$
now continue