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Infinite series doubt

  1. Aug 5, 2011 #1
    On the provided attachment, I have problem understanding the last step of the 1st sum of that page. Can anyone explain to me what is being done after the second-last step?

    Attached Files:

  2. jcsd
  3. Aug 5, 2011 #2
    They're using the formula for the sum of a finite geometric series:
    [tex]\sum_{k=1}^{n}r^k = r\frac{1-r^n}{1-r}[/tex]
  4. Aug 5, 2011 #3
    How is it a finite series? Aren't the term going till infinity? Sorry but I am actually a litle weak on my basics.
  5. Aug 5, 2011 #4
    The term s_n is the sum of just the first n terms, which is a finite series. The value of the infinite series is obtained by taking the limit of s_n as nā†’āˆž.
  6. Aug 5, 2011 #5
    Thanks! :-)
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