I have the two series:(adsbygoogle = window.adsbygoogle || []).push({});

C = 1 + (1/3)cosx + (1/9)cos2x + (1/27)cos3x ... (1/3^n)cosnx

S = (1/3) sinx + (1/9)sin2x ... (1/3^n)sinnx

I have to express, in terms of x, the sum to infinity of these two series.

Here's what I've done so far:

Let z represent cosx + jsinx

C + jS = z^0 + (1/3)Z^1 ... (1/3)^n(Z^n)

This is a GP with first term 1, common ratio (1/3)Z.

Sum to infinity of C + jS = a/(1-r) = 3/(3-Z)

I can't seem to find where to go from there. Can anyone help?

Thankyou.

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# Homework Help: Infinite series of complex numbers.

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