Summation of Trignometric Series

Thread starter Himanshu
Start date Oct 31, 2007
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Series Summation

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The discussion focuses on summing the series Sin(x) + Sin(x+d) + Sin(x+2d)...+Sin(x+(n-1)d) using the identity Sin(x) = [Exp(ix) - Exp(-ix)]/(2i). Participants suggest that this approach leads to two geometric series, which can simplify the summation process. The use of telescopic series is mentioned as a method for handling the summation of sine and cosine functions in arithmetic progression. The conversation emphasizes the importance of recognizing the geometric series formed by the exponential terms. Ultimately, the discussion aims to clarify the steps needed to compute the summation effectively.

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 don't know how to proceed. Please Help!

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Oct 31, 2007

Count Iblis

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

Then you get two ordinary geometric series.

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