# Thread: Induction question, not sure how to do this, help appreciated

1. ## Induction question, not sure how to do this, help appreciated

Use induction to show that:

(1+x) E (n, i=0) (-x)^i = 1 + x^(n+1)

The E (n, i=0) bit is the summation notation with the n on top and i=0 on the bottom, you know?

2. Originally Posted by brumby_3
Use induction to show that:

(1+x) E (n, i=0) (-x)^i = 1 + x^(n+1)

The E (n, i=0) bit is the summation notation with the n on top and i=0 on the bottom, you know?
I assume you meant you want to show $\displaystyle (x+1)\sum_{i=0}^n (-x)^i=(-1)^nx^{n+1}+1$

I leave the base case to you.

Suppose your assertion is true for $n$ i.e. $\displaystyle (x+1)\sum_{i=0}^n (-x)^i=(-1)^nx^{n+1}+1$

Now $\displaystyle (x+1)\sum_{i=0}^{n+1} (-x)^i=(x+1)(-x)^{n+1}+(x+1)\sum_{i=0}^{n+1} (-x)^i=(x+1)(-x)^{n+1}+(-1)^nx^{n+1}+1$

Can you finish up from here?