Convergence

**chaddy** · March 11th 2008, 12:39 AM

Find all x for which this series converges: from n=0 to infinity, the summation of ((-1)^n)(x)^n/(4)^n?

**mr fantastic** · March 11th 2008, 12:56 AM

Originally Posted by chaddy

Find all x for which this series converges: from n=0 to infinity, the summation of ((-1)^n)(x)^n/(4)^n?

$\sum_{n=0}^{\infty} (-1)^n \left( \frac{x}{4} \right)^n$ will converge (by the alternating series test) if $\left| \frac{x}{4} \right|^n \rightarrow 0$ as $n \rightarrow \infty$ .....

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