calculus

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test the series for convergence or divergence using the alternating series test

the sum from n=1 to infinity of (-1)^n/(3n+1)

I said it converges, is this true?

  • calculus -

    Hi:

    You are correct. The test criteria are,

    1) The terms a_n are of decreasing sequence; clearly 1/(3n+1) is decreasing on [1, inf].

    2) Limit(n->inf)[a_n] = 0.

    Both criteria having been met, we conclude convergence.

    Regards,

    Rich B.

  • calculus -

    "If the sequence An converges to 0, and each An is smaller than An-1 (i.e. the sequence An is monotone decreasing), then the series converges."

    In this case, An = 1 / (3n + 1)

    The limit as n->infinity (An) = 0

    A1 = 1 / 4
    A2 = 1 / 7

    Therefore, by the Alternating Series Test the series converges.

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