Sum of the infinite series 405-270+180-120+80

[duki]

Homework Statement

Find the sum of the infinite series: 405-270+180-120+80...

Homework Equations

??

The Attempt at a Solution

I know there's a formula for this but I can't remember it. Could someone refresh my memory?

 

[gabbagabbahey]

You'll need to start by finding the pattern between successive terms in the series... call the first term $a_0=405$ , the 2nd term $a_1=-270$ etc... so that the series can be represented as:

$405-270+180-120+80 \ldots=a_0+a_1+a_2+a_3+a_4 \ldots=\sum_{n=0}^{\infty} a_n$

There should be any easy to spot relationship between terms in the series...can you spot it?