# Thread:

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...
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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 $(-x^2)^k$.

3. Originally Posted by mr fantastic
Note that the thing you're summing can be written as $(-x^2)^k$.
What does $(-x^2)^k$ 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 $(-x^2)^k$ give me? I guess I don't quite understand what form my answer should be in when they say derive the indicated result?
If $|x|<1$ then $\sum\limits_{k = 0}^\infty {\left( { - x^2 } \right)^k } = \frac{1}{{1 + x^2 }}$
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