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Math Help - geometic series

  1. #1
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    geometic series

    A geometic series of n terms that can be written:
    a + ar + ar^2 + ar^3 + ... + ar^n-1 where a is the first term and r is the common ratio. If I express this in sigma notation would the lower limit be k=1 and the upper limit be n and the sum be r^n-1? and how would I write a forumula for this? Could I write Sn= a/(1-r) when -1 < r < +1?
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  2. #2
    Junior Member AlvinCY's Avatar
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    Quote Originally Posted by kcsteven View Post
    A geometic series of n terms that can be written:
    a + ar + ar^2 + ar^3 + ... + ar^{n-1} where a is the first term and r is the common ratio. If I express this in sigma notation would the lower limit be k = 1 and the upper limit be n and the sum be r^{n-1}? and how would I write a forumula for this? Could I write S_n= \frac{a}{1-r} when -1 < r < +1?
    You're very close with your Sigma notation, you left out the a

    a + ar + ar^2 + ar^3 + ... + ar^{n-1} = \sum_{k=1}^{n} ar^{k-1} = a \sum_{k=1}^{n} r^{k-1}

    However, I'd probably write this, they're equivalent

    a + ar + ar^2 + ar^3 + ... + ar^{n-1} = \sum_{k=0}^{n-1} ar^k = a \sum_{k=0}^{n-1} r^k

    As for S_n= \frac{a}{1-r}, that is in fact the limiting sum of a geometric sequence for |r|< 1, so yes, you're correct in that statement.

    Hope that helped
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