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Math Help - series problem

  1. #1
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    series problem

    does this converge or diverge, if it converges, to what sum.

    (2/3) - (4/9) + (8/27) - (16/81)

    so a(n) = (-1)^n * 2^(n+1)/3^(n+1)

    i know its convergent by alternating series test, but how can i figure out what sum it converges to without Sn formula?
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  2. #2
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    Quote Originally Posted by synnexster View Post
    does this converge or diverge, if it converges, to what sum.

    (2/3) - (4/9) + (8/27) - (16/81)

    so a(n) = (-1)^n * 2^(n+1)/3^(n+1)

    i know its convergent by alternating series test, but how can i figure out what sum it converges to without Sn formula?
    It is a geometric series,
    The ratio is,
    -2/3
    Which is convergent since,
    |-2/3|<1
    Now just use the infinite geometric sum formula to find the sum.
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  3. #3
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    so the sum would be a/(1-r) right?
    so (2/3)/(1-(2/3)) = 2
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  4. #4
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    Quote Originally Posted by synnexster View Post
    so the sum would be a/(1-r) right?
    so (2/3)/(1-(2/3)) = 2
    Indeed, I shall wager my soul for that!
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