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Geometric series partial sums question

  • Thread starter cue928
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  • #1
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I am looking at a geometric series problem that has already been worked out, so not assigned, but I do not see where they get a number:

Summation from n=1 to inf: 1/(n^2+4n+3)
In doing the partial sums, he has (1/2)* summation... 1/(i+1) - 1/(i+3)
I understand the breakup, but where does the "1/2" come from?
 

Answers and Replies

  • #2
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Because

[tex]\frac{1}{n+1}-\frac{1}{n+3}=\frac{2}{n^2+4n+3}[/tex]

But you want a 1 in the numerator...
 

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