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Alternating series remainder

n=1 (1)n+1n\displaystyle\sum\limits_{n=1}^{\infty }~{\frac{{{\left( -1 \right)}^{n+1}}}{n}}
Using the alternating series error test, what is the least number of terms necessary to approximate the series to within ±0.001\pm 0.001 of the actual value?
  • Your answer should be
  • an integer, like 66
  • an exact decimal, like 0.750.75
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4