# series converges?

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• March 15th 2009, 05:30 PM
twilightstr
series converges?
find the values for which the series converges. FInd the sum of the series for those values of x. sum {sn} from n = 0 to infinity. of (cos x)^n/(2^n).

my work: sum {sn} from k =1 to infinity where n = k-1. of [(cos x)/2]^ (k-1)
so the sum is 1/(1-(cosx)/2) converges for all x.

is this right?
• March 15th 2009, 05:48 PM
skeeter
I would have done a direct comparison with $\sum \frac{1}{2^n}$ to show convergence.