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Math Help - Infinite Geometric Series

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by nick898 View Post
    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.
    Write your series as

    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}}
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