How Do You Calculate the Summation of a Function from n=1 to Infinity?

[darkmagic]

Homework Statement

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

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

Homework Equations

The Attempt at a Solution

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

 

[tiny-tim]

Hi darkmagic!

(have a pi: π and an infinity: ∞ )

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

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

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(∑ e^inπt)

 

[HallsofIvy]

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