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March 26, 2017

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Find a power series whose sum is:

(a) 5 / (1-3x)

(b) 9 / (1-4x)

(c) 6 / (2-4x)

  • Pre-Cal - ,

    suppose I have

    1 + x + x^2 + x^3 + ...

    this is a geometric series with
    a = 1 and r = x
    S = a/(1-r)
    = 1/(1 - x)

    so in a) you have
    5/(1-3x)
    this would match the terms
    5 + 5(3x) + 5(3x)^2 + 5(3x)^3 + ...

    You did not state whether you have to give the answer in Sigma notation, but I am pretty sure you could change it into that notation, if you study series at this level.

    for c), simplify
    6/(2-4x) to 3/(1 - 2x) and proceed as above.

  • Pre-Cal - ,

    MY ANSWERS:

    (a) ax = 5(3x)^(x-1)

    (b) ax = 4(4x)^(x-1)

    (c) ax = 3(2x)^(x-1)

    I'm confused because all of those series have a divergent sum, and it looks like they're each supposed to be convergent.

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