Series Convergence and Sum Calculation

[mundane]

Homework Statement

Please write a specific function to define this series. Also provide a sum that the series converges to.

Homework Equations

S_n - {1, 1+1/e², 1+1/e²+1/e⁴, 1+1/e²+1/e⁴+1/e⁶, ...}

The Attempt at a Solution

I know that the common ratio is 1/e² and that you can raise that to the nth exponent for the last portion of each term, but how would I write this along with the previous parts from n-1, n-2, n-3, etc. added to it for each term? In other words, how can I show this in sigma notation and find the sum of it?

Thanks,
Dane

 

[micromass]

What do you know about geometric sequences?? Do you know how to find the sum of one?

 

[mundane]

I believe it is a1/1-r, so 1/1-(1/e^2)? But I need to know how to express this in sigma notation first. I can't figure out how to represent it.

 

[mundane]

Anyone?