# Math Help - Induction

1. ## Induction

$P(n)=1*2*3+2*3*4+..+n(n+1)(n+2)={n(n+1)(n+2)(n+3)}/{4}$

Assume P(n), then P(n+1)= $1*2*3+2*3*4+..+n(n+1)(n+2)+(n+1)(n+2)(n+3)=$ ${(n+1)(n+2)(n+3)(n+4)}/{4}$

So, P(n+1) = $1*2*3+2*3*4+..+n(n+1)(n+2)+(n+1)(n+2)(n+3)$
= ${n(n+1)(n+2)(n+3)}/{4}+(n+1)(n+2)(n+3)$
= $(k+1)(k+2)(k+3)({k}/{4}+1)$

Now I can't figure out how to get my answer to equal ${(n+1)(n+2)(n+3)(n+4)}/{4}$

2. $P(n+1) = P(n) + (n+1)(n+2)(n+3)$

$P(n+1) = \frac{n(n+1)(n+2)(n+3)}{4} + \frac{4(n+1)(n+2)(n+3)}{4}$

$P(n+1) = \frac{n(n+1)(n+2)(n+3) + 4(n+1)(n+2)(n+3)}{4}$

$P(n+1) = \frac{(n+1)(n+2)(n+3)(n + 4)}{4}$

3. ## How did you simplify that?

How did you get from

to

4. Originally Posted by jennifer1004
How did you get from

to

Factor like terms.

5. ## Thanks

Duh! I feel silly. Thanks a bunch!