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    Geometric series

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    Determine if the following series converges and if possible give its sum

    2/3 + 2/9 + 2/27 + 2/81 + ...

    © BrainMass Inc. brainmass.com December 24, 2021, 4:51 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/geometric-series-converging-11838

    SOLUTION This solution is FREE courtesy of BrainMass!

    Yes the series converges. It is an infinitie Geometric Series.

    The series can be written as :

    2/3 + (2/3)*1/3 + (2/3)*1/3^2 + (2/3)*1/3^3.......

    The sum to an infinite Geometric series is given by :

    a/(1-r) where a = first term
    r = rate.

    Putting in equation : a = 2/3 and r = 1/3 we have
    2/3/(1-1/3)
    = 2/3/(2/3)
    = 1 ( Answer).

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:51 pm ad1c9bdddf>
    https://brainmass.com/math/calculus-and-analysis/geometric-series-converging-11838

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