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    Alternating Series Test

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    (Alternating Series Test) If (a_n) is a non-increasing sequence of positive numbers and lim⁡〖a_n 〗=0, then the series ∑▒〖(-1)〗^n a_n converges.
    If the hypothesis that (a_n) is non-increasing is dropped, show or prove that the Alternating Series Test may fail.

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    Solution Summary

    Alternating Series Test is applied.