(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# United States Calculus 2 - Infinite Series

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