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Math Help - Sum of a series?

  1. #1
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    Sum of a series?

    I'm not sure how to tackle this problem:

    If the nth partial sum of a series a(n) from 1 to infinity is s(n)=3-n(2)^(-n), find a(n) and the sum of a(n) from n=1 to infinity.

    Thanks
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  2. #2
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    Quote Originally Posted by pianopiano View Post
    I'm not sure how to tackle this problem:

    If the nth partial sum of a series a(n) from 1 to infinity is s(n)=3-n(2)^(-n), find a(n) and the sum of a(n) from n=1 to infinity.

    Thanks
    So \sum_{k=1}^n a(k) = s(n) = 3-n2^{-n} right?

    Well hint for part one: Note that s(n)-s(n-1)=\sum_{k=1}^n a(k) - \sum_{k=1}^{n-1} a(k) = a(n)

    Hint for part two: \sum_{k=1}^\infty a(k) = \lim_{n\rightarrow \infty} \sum_{k=1}^n a(k) =  \lim_{n\rightarrow \infty} s(n)
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