document.write( "Question 643988: What is the sum of the first 900 consecutive odd numbers?
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Algebra.Com's Answer #404752 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
There are two ways to do it.  Here are both ways:\r\n" );
document.write( "First way (without memorizing a frmula):\r\n" );
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document.write( "The 1st odd number is 1, 1 less than 2 which is twice 1.\r\n" );
document.write( "The 2nd odd number is 3, 1 less than 4 which is twice 2.\r\n" );
document.write( "The 3rd odd number is 5, 1 less than 6 which is twice 3.\r\n" );
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document.write( "So using that pattern\r\n" );
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document.write( "The 900th odd number is 1 less than twice 900, which is 1800, so the\r\n" );
document.write( "900th odd number is 1799\r\n" );
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document.write( "Suppose the sum = N, then\r\n" );
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document.write( " N =    1 +    3 +    5 +    7 + ··· + 1793 + 1795 + 1797 + 1799\r\n" );
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document.write( "N also equals that same sum with the numbers added in the reverse order:\r\n" );
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document.write( " N = 1799 + 1797 + 1795 + 1793 + ··· +    7 +    5 +    3 +    1\r\n" );
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document.write( "Now let's write those two equations one under the other, and add equals \r\n" );
document.write( "to equals term by term:\r\n" );
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document.write( " N =    1 +    3 +    5 +    7 + ··· + 1793 + 1795 + 1797 + 1799\r\n" );
document.write( " N = 1799 + 1797 + 1795 + 1793 + ··· +    7 +    5 +    3 +    1\r\n" );
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document.write( "2N = 1800 + 1800 + 1800 + 1800 + ··· + 1800 + 1800 + 1800 + 1800\r\n" );
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document.write( "Since we know there are 900 terms on the right, that sum on the right is \r\n" );
document.write( "900 times 1800 or 1620000, so that equation bercomes\r\n" );
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document.write( "2N = 1620000\r\n" );
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document.write( "Dividing both sides by 2\r\n" );
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document.write( " N = 810000\r\n" );
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document.write( "The other way is to memorize the arithmetic series sum formula:\r\n" );
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document.write( "Sn = \"n%2F2\"[2·a1 + (n-1)·d]\r\n" );
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document.write( "Where n=900, a1=1 because it is the 1st odd integer, and d=2,\r\n" );
document.write( "because consecutive odd numbers differ by 2.\r\n" );
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document.write( "S900 = \"900%2F2\"[2·(1) + (900-1)·(2)]\r\n" );
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document.write( "S900 = 450[2 + (899)·(2)]\r\n" );
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document.write( "S900 = 450[2 + 1798]\r\n" );
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document.write( "S900 = 450[1800]\r\n" );
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document.write( "S900 = 810000\r\n" );
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document.write( "Edwin

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