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Old 2004-09-13, 19:01   #2
philmoore
 
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"Phil"
Sep 2002
Tracktown, U.S.A.

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Assuming that x is a real variable:

cos(n) = Re(e^(in)) , from Euler's formula. (Re indicates the real part of a complex number.)

Therefore, your sum is Sum(n:0 to inf) Re((e^i)^n)*x^n.
Assuming x^n is real, you can take the Re outside the sum and write this as the real part of a geometric series:
Re(Sum(n:0 to inf) ((e^i)*x)^n = Re (1/(1-(e^i)*x)
Now you just need to multiply by the complex conjugate and use the fact that e^i = cos(1) + i*sin(1)

Hope this helps!
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