series: does sum [1, infty] [ (cos1)^x ] converge?

The series \(\displaystyle \sum\limits_{k = 1}^\infty {x^k }\) converges if and only if \(\displaystyle \left| x \right| < 1\).
We know that \(\displaystyle \cos (1) \approx 0.54\) so does the series converge?
 
summergrl said:
yes! To find the sum I do 1/(1-cos1) which is about 2.17 correct?

no, the sum will be S = cos(1)/[1 - cos(1)] ... 1.175
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