Mathematics

Mathematics

Problem

Which of the following statements gives a sufficient set of conditions for the alternating series ∑n=1∞(−1)nan\sum_{n=1}^{\infty}(-1)^{n}a_{n} to converge? a) {an}\{a_n\} is positive and bounded above by 11. b) {an}\{a_n\} is eventually decreasing, but the limit of ana_n need not be 00. c) {an}\{a_n\} is eventually decreasing and lim⁡n→∞an=0\displaystyle \lim_{n\to\infty}a_n=0. d) lim⁡n→∞an=0\displaystyle \lim_{n\to\infty}a_n = 0.

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