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Alternating series remainder

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sum, start subscript, n, equals, 1, end subscript, start superscript, infinity, end superscript, start fraction, left parenthesis, minus, 1, right parenthesis, start superscript, n, plus, 1, end superscript, divided by, n, cubed, end fraction
Using the alternating series error test, what is the least number of terms necessary to approximate the series to within plus minus, 0, point, 001 of the actual value?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4