sum of sine

[Bak, ahmad]

please if some one can help me to find the summation
|y*sin(x)|+|(y^2)*sin(2x)|+...+|(y^m)*sin(mx)|
ans thanks for reading

[Luís Lopes]

Dear guauser+ahmadmath,

This is almost exercise 71 of a book that I have written (in portuguese).

To put it shortly, if f(k) = q^k sin(kx), then
F(k) = \frac{q^{k+1} sin(k-1)x - q^k sin(kx) } {1 - 2qcos(x) + q^2}.

So,

S_n(q,x) = \sum_{k=1}^n q^k sin(kx) = F(n+1) - F(1).

This is the answer if q^k sin(kx) is always \geq 0.

Hope this helps.

Luis

[Bak, ahmad]

thanks but you should notice that there are absolute values