Question

Find the smallest value $N$ for which the Alternating Series Estimation Theorem guarantees that the error $|R_N| = |S - S_N|$ of approximating the alternating series $qquad S = sum_{n=1}^{infty} frac{(-1)^n}{n^{5/2}}$ by the partial sum $qquad S_N = sum_{k=1}^N frac{(-1)^k}{k^{5/2}}$ is at most $10^{-3}$. What is this smallest value of $N$?

          Find the smallest value $N$ for which the Alternating Series Estimation Theorem guarantees that the error $|R_N| = |S - S_N|$ of approximating the alternating series
$qquad S = sum_{n=1}^{infty} frac{(-1)^n}{n^{5/2}}$
by the partial sum
$qquad S_N = sum_{k=1}^N frac{(-1)^k}{k^{5/2}}$
is at most $10^{-3}$. What is this smallest value of $N$?

$Find the smallest value N for which the Alternating Series Estimation Theorem guarantees that the error |RN| = |S - SN| of approximating the alternating series qquad S = sumn=1^infty frac(-1)^nn^5/2 by the partial sum qquad SN = sumk=1^N frac(-1)^kk^5/2 is at most 10^-3. What is this smallest value of N?$

Added by Evelyn S.

Question

Please give Ace some feedback