Mathematics

Mathematics

Problem

Which of the following infinite series satisfies all of the conditions required for the alternating series error bound to give an upper estimate for the remainder of its NN-th partial sum? a) ∑n=1∞(−1)nnn+2\displaystyle \sum_{n=1}^{\infty} (-1)^{n}\dfrac{n}{n+2} b) ∑n=1∞(−1)n−1sin⁡nn\displaystyle \sum_{n=1}^{\infty} (-1)^{n-1}\dfrac{\sin n}{n} c) ∑n=1∞(−1)n−11n\displaystyle \sum_{n=1}^{\infty} (-1)^{n-1}\dfrac{1}{n} d) ∑n=1∞(−1)n−11 n+(−1)n\displaystyle \sum_{n=1}^{\infty} (-1)^{n-1}\dfrac{1}{\,n+(-1)^{n}}

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