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find the sum of each of the following infinite series, if no sum, write no sum.

9-3+1-1/3+1/9...

1/2+1+2+4...

  • math -

    S = a/(1/r) where │r│ < 1

    in the first,
    a = 9, r = -1/3

    so sum = 9/(1 - (-1/3)) = 6.75 or 27/4

    For the second one, there is no sum, since the series diverges.
    notice r = 2, so it does not satisfy the condition for the formula.

  • math -

    Thank you.

  • typo - math -

    I just notice a typo in my formula, should of course be
    a/(1-r) where │r│ < 1

    I did use it correctly in the calculations

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