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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- Jan 29th 2009, 01:15 PMrcmangoconverging 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. - Jan 29th 2009, 02:23 PMMush
- Jan 29th 2009, 02:46 PMPlato
Think collapsing sums!

$\displaystyle \sum\limits_{k = 2}^\infty {\frac{1}

{{k\left( {k + 2} \right)}}} = \frac{1}

{2}\sum\limits_{k = 2}^\infty {\left[ {\frac{1}

{k} - \frac{1}

{{k + 2}}} \right]} \to \frac{5}

{{12}}$