Submitted by spacedino101 on Thu, 05/04/2017 - 13:17

I'm looking at the ATS solutions

It says: "Now we can sum our series, it is: " ...

But I'm not sure how you get from the 2nd line to the third?

Thanks in advance!

Submitted by spacedino101 on Thu, 05/04/2017 - 13:17

Forums:

I'm looking at the ATS solutions

It says: "Now we can sum our series, it is: " ...

But I'm not sure how you get from the 2nd line to the third?

Thanks in advance!

## You've just proven that the

You've just proven that the coefficient in of $x^r$ in $f(x)$ is $(r^2+1)$ where $f(x)$ is that ugly fraction.

That is, you've shown $f(x) =\frac{1-x+2x^2}{(1-x)^3}= (0^2+1) + (1^2 +1)x + (2^2 + 1)x^2 + \cdots + (r^2+1)x^r+ \cdots$

Can you see what happens if we put $x=1/2$ in...? What's $f(1/2)$?