- #1

- 152

- 0

## Homework Statement

Evaluate the sum [tex]2009[/tex][tex]^{2}[/tex] - [tex]2008[/tex][tex]^{2}[/tex] + [tex]2007[/tex][tex]^{2}[/tex] - [tex]2006[/tex][tex]^{2}[/tex] + ... + [tex]3[/tex][tex]^{2}[/tex] - [tex]2[/tex][tex]^{2}[/tex] + [tex]1[/tex][tex]^{2}[/tex]

## Homework Equations

I think that the equivalent series representation of this sum is:

[tex]\sum^{2009}_{n=1}n^{2}(-1)^{n+1}[/tex]

## The Attempt at a Solution

I vaguely remember in one of my calculus classes way back when something about finding the convergence of a series, I just don't remember how exactly to do it. I'm sure that is probably the easiest method to obtaining the sum. I found the sum by a somewhat roundabout method, which just consisted of finding patterns within patterns eventually reducing the 2009-part summation to a 12-part summation as follows:

435 + 21510 + 53910 + 86310 + 118710 + 151110 + 183510 +215910 + 248310 + 280710 + 313110 + 345510

resulting in a sum of 2,019,045.

Could someone who knows how to find the solution to the series please check my answer? Thanks!

Last edited: