What is an example of an infinite series that has double alternating signs?? --++--++ or ++--++--

I'm drawing a blank! Please help!

Something like: (-1)^(an expression of K)

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- May 9th 2011, 05:13 PMbetzenderferInfinite Series with Double Alternating Signs
What is an example of an infinite series that has double alternating signs?? --++--++ or ++--++--

I'm drawing a blank! Please help!

Something like: (-1)^(an expression of K) - May 9th 2011, 05:23 PMAckbeet
How about

$\displaystyle \sum_{k=0}^{\infty}\sin\left((2k+1)\,\frac{\pi}{4} \right)\,\frac{1}{x^{k}}?$