Infinite Geometric Series

• Feb 4th 2009, 03:19 PM
nick898
Infinite Geometric Series
We are told to find the sum of the following infinite geometric series:

2+1/2-1/4+1/8-1/16...

I went to my professor earlier today and saw how he manipulated the series. (He replaced 2 with 3-1) Unfortunately, I had a class right after I met with him so afterwards I forgot what he showed me. He told me to try to manipulate it in a way so that you see a series that looks like:

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

For the life of me I can't seem to find the spot where we left off together.
• Feb 4th 2009, 03:24 PM
Jester
Quote:

Originally Posted by nick898
We are told to find the sum of the following infinite geometric series:

2+1/2-1/4+1/8-1/16...

I went to my professor earlier today and saw how he manipulated the series. (He replaced 2 with 3-1) Unfortunately, I had a class right after I met with him so afterwards I forgot what he showed me. He told me to try to manipulate it in a way so that you see a series that looks like:

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

For the life of me I can't seem to find the spot where we left off together.

$1 + \underbrace{1 + \frac{1}{2} - \left( \frac{1}{2}\right)^2 + \left( \frac{1}{2}\right)^3- \left( \frac{1}{2}\right)^4 \cdots }_{\text{this is geometric}}$