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Math Help - sum of the series

  1. #1
    Junior Member
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    Smile sum of the series

    I am asked to use this formula: Sn = a/1-r for |r|<1 To solve this problem:
    (1.07) + (1.07)^2 + (1.07)^3 + ...+(1.07)^60
    I was trying to think of this in terms of sigma notation where we have a lower and upper limit and then raising it to a power to get the sum. I can see the exponent changing from 0 to 60 and a common ratio of (1.07). I tried putting it into the calculator as sum(seq(1.07x,x,0,60) =1958.1 but I am not sure how that helps me. I guess I am a little lost, could someone put me in the right direction.
    Thank you,
    Keith Stevens
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  2. #2
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    Hello, Keith!

    I am asked to use this formula: Sn = a/(1-r) for |r|<1 to solve this problem:
    . . (1.07) + (1.07)^2 + (1.07)^3 + ...+(1.07)^60
    Wrong formula!

    That formula is for an infinite geometric series.
    . . This series is not infinite; it has only 61 terms.


    For a geometric series with n terms, the formula is:

    . . . . . . . . . . . 1 - r^n
    . . . S_n . = . a --------
    . . . . . . . . . . . . 1 - r

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  3. #3
    Forum Admin topsquark's Avatar
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    There is an additional problem with kcsteven's formula that I think is important to mention. To use S = a/(1-r), we require that |r| < 1, whereas in his series r = 1.07.

    -Dan
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