# Thread: Induction Proof

1. ## Induction Proof

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.

2. Originally Posted by shawn
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.

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 $P(n)$: " $3^n + 4^n \le 5^n$ for all $n \in \mathbb{N},~n \ge 2$"

So, $P(2)$: $3^2 + 4^2 = 9 + 16 = 25 \le 5^2$

so, $P(2)$ holds.

Assume $P(n)$ holds for some $n \ge 2$, we show $P(n + 1)$

now continue