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Math Help - Telescoping series Question

  1. #1
    s3a
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    Telescoping series Question

    I am having trouble with this question: sum 4/(n*(n+2)) from n = 1 to inf - Wolfram|Alpha

    (My work is attached)

    The correct final answer is: 3.

    Any help would be greatly appreciated!
    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Telescoping series Question-temp_q.jpg  
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  2. #2
    MHF Contributor
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    Write out the first 4 terms and you should see it.

    (\frac{2}{1}-\frac{2}{3})+(\frac{2}{2}-\frac{2}{4})+(\frac{2}{3}-\frac{2}{5})+...+(\frac{2}{n}-\frac{2}{n+2})

    You are left with: 2+1+\lim_{n\rightarrow \inf }(\frac{2}{n}-\frac{2}{n+2})
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