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 2004-09-13, 19:01 #2 philmoore     "Phil" Sep 2002 Tracktown, U.S.A. 100010111112 Posts 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!