document.write( "Question 1103595: Please find the limit of the following sequence as n goes to infinity:\r
\n" ); document.write( "\n" ); document.write( " $\"n%2F%28n%5E2%2B1%29+%2Bn%2F%28n%5E2%2B4%29%2B+n%2F%28n%5E2%2B9%29\"$ +...+ $\"n%2F%28n%5E2%2B%28n-1%29%5E2%29%2B1%2F%282n%29\"$ .\r
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Algebra.Com's Answer #720093 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!
Sorry, not a closed form solution, but some values as n gets \"large\"Е
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\n" ); document.write( "Let $\"+S%5Bn%5D+\"$ = Partial sum n, $\"+n%3E=+1+\"$
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\n" ); document.write( "\n" ); document.write( " $\"+S%5B1%5D+=+1%2F2+=+0.5+\"$
\n" ); document.write( " $\"+S%5B2%5D+=+0.65+\"$
\n" ); document.write( " $\"+S%5B3%5D+=+0.6974359+\"$
\n" ); document.write( ": : :
\n" ); document.write( " $\"+S%5B1000%5D+=+0.7851481+\"$
\n" ); document.write( ": : :
\n" ); document.write( " $\"+S%5B10000%5D+=+0.7853732+\"$
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\n" ); document.write( " $\"+S%5B100000%5D+=+0.7853957+\"$
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\n" ); document.write( " $\"+S%5B1000000%5D+=+0.7853979+\"$
\n" ); document.write( "ЧЧЧЧЧЧЧЧЧЧ\r
\n" ); document.write( "\n" ); document.write( "Values found using a Perl one-liner (if you have Perl installed, edit the value of $m to set the max value)
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\n" ); document.write( "\n" ); document.write( "perl -e '$m=1000000; for($i=0, $s=0; $i<$m; $i++) { $s += $m/($m*$m+($i+1)*($i+1)); }; print \"Sum = $s\n\";'
\n" ); document.write( "Sum = 0.785397913397392
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