# Thread: sin(x + y) + sin(x + 2y) + sin(x + 3y) +...+ sin(x + ny) ???

1. What is [sin(x + y) + sin(x + 2y) + sin(x + 3y) +...+ sin(x + ny)] equal to?
The angles are in arithmetic progression....

Help required urgently!!

2.

3. As this looks like homework, I urge you to read this

4. Then all you have to do is simplify the RHS and equate imaginary parts.

5. I'm impressed!

6. That’s pretty much the standard way of computing the sum of the sines or cosines of an arithmetic progression of angles.

Another way is to use a telescoping formula – but for this you may need to be smart enough to find a formula that fits.

7. I know it's the standard way, but I expected it to take a few more lines than that. I'm going to try out the telescoping way now.

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