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Math Help - sequence converge or diverge

  1. #1
    VkL
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    sequence converge or diverge

    Does the sequence converge or diverge? If the sequence converges, to what value?

    ( (-0.1)^n ) / n


    The Limit if this goes to zero, so it must converge i'm assuming. ??
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    Quote Originally Posted by VkL View Post
    The Limit if this goes to zero, so it must converge i'm assuming. ??
    If the limit is zero, then the sequence converges to zero. This is by definition.

    And in this case we do have

    \lim_{n\to\infty}\frac{(-0.1)^n}n

    =\lim_{n\to\infty}\frac{(-1/10)^n}n

    =\lim_{n\to\infty}(-1)^n\frac{1/10^n}n

    =\lim_{n\to\infty}(-1)^n\frac1{n10^n}

    =0.
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