# Induction Emergency!

• Sep 11th 2008, 03:57 PM
juldancer
Induction Emergency!
I have a test tomorrow and I'm really confused on induction. I was able to figure out one of my homework problems, but I'm having trouble with this one:

Directions - Use mathematical induction to prove the given formula for every positive integer n.

http://i7.photobucket.com/albums/y29...er17/math1.png
I could really use help! Thanks!
• Sep 11th 2008, 05:08 PM
skeeter
$\sum_{i=1}^{n+1} i(i+1) =$

$\left[ \sum_{i=1}^n i(i+1) \right] + (n+1)(n+2) =$

$\frac{n(n+1)(n+2)}{3} + (n+1)(n+2) =$

$\frac{n(n+1)(n+2)}{3} + \frac{3(n+1)(n+2)}{3} =$

$\frac{n(n+1)(n+2) + 3(n+1)(n+2)}{3} =$

$\frac{(n+1)(n+2)(n + 3)}{3} = \sum_{i=1}^{n+1} i(i+1)$