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Math Help - finding a formula for partial sums geometic series

  1. #1
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    finding a formula for partial sums geometic series

    could someone try to explain how to go about this process? i can find the sum of a series with no problem, i can find the equation for that, but i am completely lost as to how to create a formula to find the nth partial sum.
    so given this sequence of numbers:
    2+ 2/3 + 2/9 + 2/27 + .... how do i find the formula for the nth partial sum?
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  2. #2
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    Quote Originally Posted by isuckatcalc View Post
    could someone try to explain how to go about this process? i can find the sum of a series with no problem, i can find the equation for that, but i am completely lost as to how to create a formula to find the nth partial sum.
    so given this sequence of numbers:
    2+ 2/3 + 2/9 + 2/27 + .... how do i find the formula for the nth partial sum?
    2\left(\frac{1}{3^0} + \frac{1}{3^1} + \frac{1}{3^2} + \frac{1}{3^3} + ... + \frac{1}{3^n}\right)<br />

    2\sum_{i=0}^n \left(\frac{1}{3}\right)^i
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  3. #3
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    Well, I could be wrong here, but looks to me that you're series is going \frac{2}{3^n} n=0,1,2,...
    Then the sum for the nth would be
    \sum_{i=1}^n \frac{2}{3^i} = 2\sum_{i=1}^n \frac{1}{3^i} (by taking the factor 2 outside of the summation)
    Then the above is a geometric series
    ie 2\sum_{i=1}^n \frac{1}{3^i} = 2\frac{1-\frac{1}{3}^{n+1}}{1-\frac{1}{3}} (I think that's correct but I can't remember the exact formula for a geometric summing series)

    Edit: beaten to it
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