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Math Help - converging sequence?

  1. #1
    Senior Member
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    converging sequence?

    The sequence is defined by A1 = 1

    ImageShack - Image Hosting :: 12426930zg2.jpg

    for n >= 1 is decreasing.

    and positive for all n.

    need to show it converges.

    this is a sequence, not a series.

    So i'm confused as to what test i use?

    thanks.
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  2. #2
    Super Member
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    Quote Originally Posted by rcmango View Post
    The sequence is defined by A1 = 1

    ImageShack - Image Hosting :: 12426930zg2.jpg

    for n >= 1 is decreasing.

    and positive for all n.

    need to show it converges.

    this is a sequence, not a series.

    So i'm confused as to what test i use?

    thanks.
     \displaystyle \sum_{i = 2}^{\infty} \frac{1}{i(i+2)} converges, if:

     \int_2^{\infty} \frac{dx}{x(x+2)} has a finite value.
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  3. #3
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    Think collapsing sums!
    \sum\limits_{k = 2}^\infty  {\frac{1}<br />
{{k\left( {k + 2} \right)}}}  = \frac{1}<br />
{2}\sum\limits_{k = 2}^\infty  {\left[ {\frac{1}<br />
{k} - \frac{1}<br />
{{k + 2}}} \right]}  \to \frac{5}<br />
{{12}}
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