# Summation with infinity

1. Nov 21, 2009

### darkmagic

1. The problem statement, all variables and given/known data

what is the summation of a function where n=1 to n=infinity?

For example, given a function sin[(pi)nt].

2. Relevant equations

3. The attempt at a solution

I asking how I get that
I do not know what should I do

2. Nov 22, 2009

### tiny-tim

Hi darkmagic!

(have a pi: π and an infinity: ∞ )
It's a different method in each case …

just choose the one that seems easiest.

In this case, either sum from n = 1 to N, and use the standard trigonometric identities for (sinA + sinB) etc, or (even easier ) write it as Im(∑ einπt)

3. Nov 22, 2009

### HallsofIvy

Staff Emeritus
That is a Fourier series which is a huge field of mathematics in itself.