# Math Help - Prove divisibility by induction

1. ## Prove divisibility by induction

Prove that n^3+2n is divisible by 3.

2. Originally Posted by cityismine
Prove that n^3+2n is divisible by 3.
We're going to try this with LaTeX and hope for the best.

Case 1: n = 1
$1^3 + 2 \cdot 1 = 1 + 2 = 3$
Check!

Now assume the theorem is true for n = k. We need to show it is true for n = k + 1. So we assume
$k^3 + 2k = 3a$
where a is an integer.

Thus we need to show the same for
$(k + 1)^3 + 2(k + 1)$

$= k^3 + 3k^2 + 3k + 1 + 2k + 2$

$= (k^3 + 2k) + (3k^2 + 3k + 3)$

The first term is divisible by 3 due to our assumption at n = k. The second term is obviously divisible by 3.

etc, etc.

-Dan

3. That sort of makes sense to me, but I still don't understand induction very well. It's the last chapter in my pre-calculus textbook. Do I need to learn it well for 1st year calculus?