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Homework Help: Sequence of 3/4^(2k). Show is convergent, find sum

  1. Jan 25, 2014 #1

    939

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    1. The problem statement, all variables and given/known data

    Consider the sequence ak = (3)/(4^(2k)). Show is convergent, find sum. Please check work.

    2. Relevant equations

    ak = 3/(4^2k)

    let s {n} be the series associated with the sequence. Cannot write summation notation here, but k starts at 1 (k = 1 on bottom) and infinity on top.

    3. The attempt at a solution

    ak1 = 0.1875
    ak2 = 0.01171875
    ak3 = 0.000732421876
    ak4 = 0.00004577636719

    ak4/ak3 = 0.0625

    Convergence: 1) r = 0.0625. r < 1, ∴ convergent
    Sum: 2) (0.1875)/(1-0.0625) = 0.2. Sum is 0.2
     
    Last edited: Jan 25, 2014
  2. jcsd
  3. Jan 25, 2014 #2

    ehild

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    Homework Helper

    It is correct, if the summation starts with k=1.

    ehild
     
  4. Jan 25, 2014 #3

    939

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    Thanks! Yes, it does.
     
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