Summation of Trignometric Series

1. Oct 31, 2007

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 dont know how to proceed. Please Help!

2. Oct 31, 2007

Count Iblis

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

Then you get two ordinary geometric series.