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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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.
Think collapsing sums!
$\displaystyle \sum\limits_{k = 2}^\infty {\frac{1}
{{k\left( {k + 2} \right)}}} = \frac{1}
{2}\sum\limits_{k = 2}^\infty {\left[ {\frac{1}
{k} - \frac{1}
{{k + 2}}} \right]} \to \frac{5}
{{12}}$