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Old 2004-09-13, 16:28   #1
Orgasmic Troll
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Jul 2003

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Default Question about a power series

I was playing around with some power series stuff, and I wondered what I would get if I used cos(n) as the coefficient, and I was thinking it might not converge or it might be a pathological function or something .. I plugged it into excel and got some rough estimations, and it seemed to converge between -1 and 1, graphing a smooth curve

I ended up plugging the series into Mathematica and after some tweaking, I got

Sum(n:0 to inf) cos(n)x^n = (cos(1)x - 1) / (-x^2 + 2cos(1)x - 1)

now .. how would you go about finding that out with pencil and paper?
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