SOLUTION: Please find the limit of the following sequence as n goes to infinity:
{{{n/(n^2+1) +n/(n^2+4)+ n/(n^2+9)}}}+...+ {{{n/(n^2+(n-1)^2)+1/(2n)}}}.
Thank you!
Algebra ->
Sequences-and-series
-> SOLUTION: Please find the limit of the following sequence as n goes to infinity:
{{{n/(n^2+1) +n/(n^2+4)+ n/(n^2+9)}}}+...+ {{{n/(n^2+(n-1)^2)+1/(2n)}}}.
Thank you!
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Question 1103595: Please find the limit of the following sequence as n goes to infinity:
+...+ .
Thank you! Found 2 solutions by math_helper, robertb:Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website! Sorry, not a closed form solution, but some values as n gets "large"…
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Let = Partial sum n,
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: : :
: : :
: : :
: : :
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Values found using a Perl one-liner (if you have Perl installed, edit the value of $m to set the max value)
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perl -e '$m=1000000; for($i=0, $s=0; $i<$m; $i++) { $s += $m/($m*$m+($i+1)*($i+1)); }; print "Sum = $s\n";'
Sum = 0.785397913397392
