# A Series of Even numbers squared

1. Mar 1, 2013

### hms.tech

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

Is there a general formula for the sum of such a series (or can it be self derived) ?

2^2 + 4^2 + 6^2 + 8^2 ..... N^2 (all the way till some even number N)
2. Relevant equations

$\sum r^2$ (from r=1 to r=N) = 1/6 * n(n+1)(2n+1)

3. The attempt at a solution

No clue where to start.

2. Mar 1, 2013

### Staff: Mentor

Do all the terms have a common factor that you can pull out?

3. Mar 2, 2013

### hms.tech

Oh... I did not see that. Great thinking !

After taking 2^2 common we will get a simple sequence :

1^2 + 2^2 + 3^2 + 4^2 ....

I think I get it !