document.write( "Question 1035284: [n(sigma)r=1] $\"1%2F%28r%28r%2B2%29%29\"$ =[n(sigma)r=1] $\"%281%2F2%29%28%281%2Fr%29-%281%2F%28r%2B2%29%29%29\"$
\n" ); document.write( "= $\"%281%2F2%29%28%281%2F1%29%2B%281%2F2%29-%281%2F%28n%2B1%29%29-%281%2F%28n%2B2%29%29%29%29\"$
\n" ); document.write( "Please show me more detailed steps, especially between the last two steps. \n" ); document.write( "

Algebra.Com's Answer #650015 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is what you call a telescoping series.\r
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\n" ); document.write( "\n" ); document.write( "= $\"1%2F2\"$ ( $\"1-1%2F3+%2B1%2F2+-+1%2F4+%2B+1%2F3+-+1%2F5\"$ +...+ $\"1%2F%28n-2%29-1%2Fn+%2B+1%2F%28n-1%29+-+1%2F%28n%2B1%29+%2B+1%2Fn+-+1%2F%28n%2B2%29\"$ )\r
\n" ); document.write( "\n" ); document.write( "= $\"%281%2F2%29%281+%2B+1%2F2+-1%2F%28n%2B1%29+-+1%2F%28n%2B2%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "= $\"3%2F4+-+%282n%2B3%29%2F%282n%5E2%2B6n%2B4%29\"$ \n" ); document.write( "

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