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Partial sum of geometric series

  1. Jun 6, 2009 #1
    ok so i know how to calculate the partial sum of a geometric series.

    But lets say i only want to calculate the sum of every other term, how would i do this?


    .5^0+.5^1+.5^2+...+.5^n = (.5^(n+1) - 1)/(.5-1)

    but what equation can i use to get the sum of only these terms:

    .5^1+.5^3+.5^5...+.5^n where n is odd
  2. jcsd
  3. Jun 6, 2009 #2


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    See if you can re-write it as another geometric series, utilizing that an odd number n=2m+1, for m integer.
  4. Jun 6, 2009 #3
    yea i actually need to do it for the even ones for my equation haha

    ok so i think i got it, not going to write it all out because i;m busy, but thank you :)
  5. Jun 6, 2009 #4


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    And, of course, (.5)n, for n, even, n= 2m, is (.25)m so you have just another geometric series.
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