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Homework Help: Need help writing this as a sum

  1. Jan 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Write as a series to represent the infinite sum and write the sum as a rational number.

    0.71 + 0.7171 + 0.717171 + 0.71717171...

    Please help with this problem. I have been working on it for almost an hour.
  2. jcsd
  3. Jan 4, 2010 #2


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    Gold Member

    Are you sure that you've written the problem and/or sum correctly because the particular sum in question (0.71 + 0.7171 + 0.717171 + ...) diverges and consequently is not equal to any real number. Do you perhaps mean write the decimal 0.7171... as an infinite sum and then write this sum as a rational number?
  4. Jan 9, 2010 #3
    [tex]\sum[/tex] Ak-1+.71*10-k-(k-1)

    Starting on k=2, going to n, and assuming Ak=.71 when k=1

    I'm pretty sure about this...
  5. Jan 15, 2010 #4
    [tex]\infty[/tex] i
    [tex]\Sigma[/tex] [tex]\Sigma[/tex] 71*10^(-2a)
    i = 1 a = 1

    Of this, I am certain. a=1 should be under the second summation.
  6. Jan 15, 2010 #5


    Staff: Mentor

    I'm with jgens on this. As you have written it, this is a divergent series, so doesn't represent any real number.

    Please give us the problem in its exact wording.
  7. Jan 15, 2010 #6


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    Science Advisor

    Okay, if you are certain that is the problem, then I am certain if does NOT converge.
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