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[tex]\sum_{n=-N}^{+N} cos(\alpha -nx)=cos\alpha \frac{sin(N+0.5)x}{sin(x/2)}[/tex]

[tex]\sum_{n=-N}^{+N} cos(\alpha)cos(nx)+\sum_{n=-N}^+Nsin(\alpha)\frac{sin(N+0.5)x}{sin(x/2)}[/tex]

[tex]\sum_{n=-N}^{+N}sin(\alpha)\frac{sin(N+0.5)x}{sin(x/2)} =0[/tex]

[tex]cos(\alpha) 2 \sum_{n=0}^{+N} cos(nx)[/tex]

I know of a rule that shows...

[tex]\frac{1}{2}+cos(x)+cos(2n)+...cos(nx)=\frac{sin(N+0.5)x}{2sin(x/2)}[/tex]

but I dont see how to apply it to get my answer, since my summation is similar to equation (9) on this site: http://mathworld.wolfram.com/Cosine.html

any ideas?

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# Homework Help: Summation equation help

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