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United States Calculus 2 - Infinite Series

  1. Oct 29, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than 10^-5. Although you do not need it, the exact value of the series is given.

    ln(128) = 7*sum[k=1,inf] of (-1)^(k+1)/k

    2. Relevant equations

    3. The attempt at a solution[/b

    | ln(128) - 7*sum[k=1,n] of (-1)^(k+1)/k | < 1/10,000
    subtracted ln(128) from both sides
    |-7*sum[k=1,n] of (-1)^(k+1)/k | < 1/10,000 - ln(128)
    simplified the negative on the left hand side and absolute value
    7*sum[k=1,n] of 1/k < 1/10,000 - ln(128)
    divided through by 7
    sum[k=1,n] of 1/k < 1/70,000 - ln(128)/7

    I'm unsure were to go from here, thank you for any help you can provide me.
  2. jcsd
  3. Oct 29, 2011 #2


    Staff: Mentor

    There's a remainder theorem for alternating series. Take a look at it.
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