- #1
UrbanXrisis
- 1,196
- 1
I am to show that...
[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 don't 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?
[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 don't 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?