Summation of Trignometric Series

[Himanshu]

Sum the following:

Sin(x) + Sin(x+d) + Sin(x+2d)...+Sin(x+(n-1)d).

I only know that summation of Sin and Cos functions whose arguments are in Arithmetic Progression can be done through telescopic series. But I don't know how to proceed. Please Help!

 

[Count Iblis]

Use the identity: Sin(x) = [Exp(ix) - Exp(-ix)]/(2i)

Then you get two ordinary geometric series.