document.write( "Question 1086342: The sum of the ﬁrst n integers 1 + 2 + 3 + ... + n =
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Algebra.Com's Answer #700515 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Multiply through by 2:\r\n" );
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document.write( "Use the quadratic formula to find the critical numbers\r\n" );
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document.write( "That is approximately 1413.713651, between integers 1413 and 1414\r\n" );
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document.write( "So the sum of the first 1413 positive integers is less than 1000000,\r\n" );
document.write( "and the sum of the first 1414 integers integers is more than 1000000.\r\n" );
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document.write( "To show this we substitute 1413 and 1414 in \r\n" );
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document.write( "Why cant the sum ever equal 100000.\r\n" );
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document.write( "Suppose for contradiction, that it can = 100000\r\n" );
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document.write( "Use the quadratic formula to solve for n\r\n" );
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document.write( "That's not a positive integer, so that contradicts\r\n" );
document.write( "our assumption that it could equal to a positive\r\n" );
document.write( "integer.  So the sum of the first 446 integers is\r\n" );
document.write( "less than 100000 and the sum of the first 447\r\n" );
document.write( "integers is more than 100000.\r\n" );
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document.write( "To show this we substitute 446 and 447 in \r\n" );
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document.write( "So the sum can never be 100000.\r\n" );
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document.write( "Edwin

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