# Math Help - help

1. ## help

I want to solve this exercises but I can n't ,can you help me please?

I want to find sum of functions series , and 'i' here is an index.

2. Originally Posted by suliman
I want to solve this exercises but I can n't ,can you help me please?

I want to find sum of functions series , and 'i' here is an index.

Well lets assume that for 1 you mean:

$s(n)=\sum_{i=1}^n \left( \frac{1}{x^{2i+1}}- \frac{1}{x^{2i-1}}\right)\ \ \ x \in (0,1]$

( $x$ cannote be $0$ as then the summands are undefined)

Then:

$
s(n)=\sum_{i=1}^n \frac{1}{x^{2i}} \left( \frac{1}{x}- x\right)
$

...... $=\left( \frac{1}{x}- x\right)\sum_{i=1}^n \frac{1}{x^{2i}}=\left( \frac{1}{x}- x \right) \left( \frac{1-x^{-2(n+1)}}{1-x^{-2}} \right),\ \ \ x \ne 1$

and $s(n)=0$ if $x=1$

RonL