document.write( "Question 1050865: What is 1-2+3-4+5-6+...+2013?\r
\n" ); document.write( "\n" ); document.write( "I have no idea how to do this problem. The answer is 1007\r
\n" ); document.write( "\n" ); document.write( "Any help is appreciated. Thank you!! \n" ); document.write( "

Algebra.Com's Answer #666509 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"1-2%2B3-4%2B5-6\"$ +...+ $\"2013\"$ ....take a look at signs: positive, negative, positive,negative..
\n" ); document.write( " $\"odd\"$ integers are positive and $\"even\"$ integers are negative\r
\n" ); document.write( "\n" ); document.write( "there is $\"2013\"$ integers in all
\n" ); document.write( "since first and last $\"odd\"$ integers, means there is $\"one\"$ $\"+even\"$ integer $\"less\"$ than odd\r
\n" ); document.write( "\n" ); document.write( "since $\"2013\"$ is not divisible by $\"2\"$ we can write it as $\"1007%2B1006+\"$ where $\"1007\"$ are odd integers and $\"1006\"$ even integer
\n" ); document.write( "since even integers are negative\r
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\n" ); document.write( "\n" ); document.write( "SUM OF EVEN NUMBERS: $\"n%5Be%5D%28n%5Be%5D%2B1%29\"$
\n" ); document.write( "SUM OF ODD NUMBERS: $\"n%5Bo%5D%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "since $\"even\"$ integers are negative, we subtract the sum of even from the sum of odd integers
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\n" ); document.write( " $\"n%5Bo%5D%5E2-n%5Be%5D%28n%5Be%5D%2B1%29\"$ ........... $\"n%5Be%5D=1006\"$ and $\"n%5Bo%5D=1007\"$ and we have
\n" ); document.write( "= $\"+1007%5E2-1006%281006%2B1%29\"$
\n" ); document.write( "= $\"1007%5E2-1006%281006%2B1%29\"$
\n" ); document.write( "= $\"1014049-1006%5E2-1006\"$
\n" ); document.write( "= $\"1014049++-1012036-1006\"$
\n" ); document.write( "= $\"1014049++-1013042\"$
\n" ); document.write( "= $\"1007\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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