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
Check!
Now assume the theorem is true for n = k. We need to show it is true for n = k + 1. So we assume
where a is an integer.
Thus we need to show the same for
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