Originally Posted by

**WannaBe** And about the first question...:

The series actually goes from 1 to infinity...

Hence:

$\displaystyle \sum_{n=1}^{\infty} (1-x)^2 x^n = \frac{x}{1-x} $

And:

$\displaystyle A(N,x)=\left| \left(\sum_{n=0}^N (1-x)^2 x^n\right) - \frac{x}{1-x} \right|$

If we simplify a little bit, we'll get:

$\displaystyle \sum_{n=1}^{N} (1-x)^2x^n =$

$\displaystyle \frac{(1-x)^2x(x^N-1)}{x-1}=$

$\displaystyle (x-1)x(x^N-1)=(x^N-x)(x-1)=x^{n+1}-x^N-x^2+x$ and then:[/tex]

$\displaystyle A(N,x)=\left| (\sum_{n=0}^N (1-x)^2 x^n) - \frac{x}{1-x} \right|=$

$\displaystyle \left| (x^{N+1}-x^N-x^2+x)(1-x)-x \right|=$

And I've no idea what should I do from here on....

I hope you'll be able to help me....

Thanks