Example 8-2-17 - Maple Help



Chapter 8: Infinite Sequences and Series



Section 8.2: Series

Example 8.2.17



 a) Show that Leibniz' theorem (see Table 8.2.2) on the convergence of alternating series applies to the  series $\sum _{n=1}^{\infty }\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\frac{{\left(-1\right)}^{n+1}}{\sqrt{n}}$.
 b) Obtain the first few, but graph the first 50, partial sums.
 c) If ${S}_{k}$ is the partial sum of the first $k$ terms, what value of $k$ will guarantee that the error in ${S}_{k}$ is no worse than ${10}^{-3}$?







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