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Thread: Alternating Series Sums

  1. #1
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    Alternating Series Sums

    How many terms (at least) of the alternating series E from n=1 to infinity (-1)^(n+1) 1/(n^2) must we add to be sure that the partial sum S(N) approximates the sum S of the series with error less than 0.0001?

    (a) 10
    (b) 50
    (c) 100
    (d) 120
    (e) 150
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  2. #2
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    Quote Originally Posted by leilani13 View Post
    How many terms (at least) of the alternating series E from n=1 to infinity (-1)^(n+1) 1/(n^2) must we add to be sure that the partial sum S(N) approximates the sum S of the series with error less than 0.0001?

    (a) 10
    (b) 50
    (c) 100
    (d) 120
    (e) 150
    alternating series w/ decreasing terms to 0 ... error < |first omitted term|

    error < \frac{1}{n^2} < \frac{1}{10000}

    so ... what n will work?
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  3. #3
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    100?
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  4. #4
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    Quote Originally Posted by leilani13 View Post
    100?
    you don't sound so sure ...
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  5. #5
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    I didn't understand where
    Quote Originally Posted by skeeter View Post
    error < \frac{1}{n^2} < \frac{1}{10000}
    came from. But, I understand now.
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