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Math Help - Infinite series problem?

  1. #1
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    Infinite series problem?

    Please help me for this problem.
    Test the alternate series for absolute converges or conditionally converges or diverges.
    ∑(0 to ∞)(-1)^n [π/2 - arc tan(n)]
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    (i) u_n =( pi/2 - arctan n ) -> 0 as n -> +infty . (ii) u_n is decreasing. So, the series is convergent.

    For the absolute convergence, compare u_n with v_n=1/n .
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