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!

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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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

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

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