sum of 1+cos(x)+...+cos(nx)

**livan1** · November 14th 2009, 12:41 PM

hi
i have little problem here with this problem

i have to find a formula for this sum serie

1+cos(x)+cos(2x)+cos(3x)+....+cos(nx)

the hint is i have to use sum of geometric series with the general term e^(ikX)

thanks

**Krizalid** · November 14th 2009, 03:23 PM

there's other way of doing this, or are you really asked to do it by using that hint?

**livan1** · November 14th 2009, 11:25 PM

i solved it with the hint
thanks any way

**Jhevon** · November 14th 2009, 11:29 PM

Originally Posted by livan1

i solved it with the hint
thanks any way

good job. the trick of course was to realize that your sum is the real part of the sum $\sum_{k = 0}^\infty e^{i(kx)}$ , which can be interpreted as a geometric series for which you know the formula.

Originally Posted by Krizalid

there's other way of doing this, or are you really asked to do it by using that hint?

just for fun (and curiosity) what other ways were you thinking of, Kriz?

**Krizalid** · November 15th 2009, 12:01 PM

http://www.mathhelpforum.com/math-he...m-sin-n-n.html

post #11.

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