document.write( "Question 1209331: Hi
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document.write( "Find the value of 1-2+3-4+5-6+.....+2007-2008+2009-2010+2011. \n" );
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Algebra.Com's Answer #848380 by ikleyn(52858) You can put this solution on YOUR website! .\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "This problem admits simple mathematical mental solution.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Group the terms in pairs\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "1-2+3-4+5-6+.....+2007-2008+2009-2010+2011 = (1-2)+(3-4)+(5-6)+.....+(2007-2008)+(2009-2010)+2011.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "You have 2010/2 = 1005 pairs and the last unpaired term 2011.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Each pair produces -1, so the total expression is -1005+2011, and you can calculate it mentally.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "ANSWER. 1006.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Solved (mentally)\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "This problem is specially designed to be solved in this way.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |