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Math Help - series converges?

  1. #1
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    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?
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  2. #2
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    I would have done a direct comparison with \sum \frac{1}{2^n} to show convergence.
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