document.write( "Question 1050865: What is 1-2+3-4+5-6+...+2013?\r
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Algebra.Com's Answer #666517 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Group the numbers in the series in pairs:\r\n" );
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document.write( "1 - 2 + 3 - 4 + 5 - 6 + . . . + 2013 = \r\n" );
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document.write( "(1-2) + (3-4) + (5-6) + . . . + (2011-2012) + 2013\r\n" );
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document.write( "The last number, 2013, is without pair.\r\n" );
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document.write( "Notice that every difference in parentheses is equal to -1.\r\n" );
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document.write( "How many pairs do you have ?   = 1006.\r\n" );
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document.write( "So, you have the sum of 1006 terms of \"-1\" plus 2013, which is -1006 + 2013.\r\n" );
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document.write( "Add the last two numbers.\r\n" );
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document.write( "And compare with the answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This problem is actually for low grade (young !) students who may not know about the sum of arithmetic progression.\r
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\n" ); document.write( "\n" ); document.write( "This problem is to develop their combinatoric skills.\r
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