# Thread: Appealing to geometric series

1. ## Appealing to geometric series

Derive the indicated result by appealing to the geometric series:

I know that there is something in geometric series that deal with a number being greter than or less than to 1, such as |x|<1 so I know the series must converge, but to what? I know it will converge to a value less than 1...

2. Originally Posted by WartonMorton
Derive the indicated result by appealing to the geometric series:

I know that there is something in geometric series that deal with a number being greter than or less than to 1, such as |x|<1 so I know the series must converge, but to what? I know it will converge to a value less than 1...
Note that the thing you're summing can be written as $\displaystyle (-x^2)^k$.

3. Originally Posted by mr fantastic
Note that the thing you're summing can be written as $\displaystyle (-x^2)^k$.
What does $\displaystyle (-x^2)^k$ give me? I guess I don't quite understand what form my answer should be in when they say derive the indicated result?

4. Originally Posted by WartonMorton
What does $\displaystyle (-x^2)^k$ give me? I guess I don't quite understand what form my answer should be in when they say derive the indicated result?
If $\displaystyle |x|<1$ then $\displaystyle \sum\limits_{k = 0}^\infty {\left( { - x^2 } \right)^k } = \frac{1}{{1 + x^2 }}$