# Summation of n^2k. k = 1 to infinity

1. Oct 5, 2005

### KataKoniK

Is the summation of k = 1 to infinity for n2k equal to
n2 / (1 - n2)?

2. Oct 5, 2005

### amcavoy

Yes it is (for 0<=n<1).

Alex

3. Oct 5, 2005

### KataKoniK

Thanks for the confirmation.

4. Oct 6, 2005

### HallsofIvy

Staff Emeritus
Indeed, that is just a geometric sequence with common ratio n2.

(I will confess that my first thought was that n must mean a positive integer, for which, of course, this does not converge!)