In Exercises use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.001.

Data from in Theorem 9.15

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THEOREM 9.15 Alternating Series Remainder If a convergent alternating series satisfies the condition an+1 ≤ a, then the absolute value of the remainder Ry involved in approximating the sum S by SN is less than (or equal to) the first neglected term. That is, ISSN| = |RN| ≤aN+1• A proof of this theorem is given in Appendix A. See LarsonCalculus.com for Bruce Edwards's video of this proof.