document.write( "Question 1054887: SUM THIS SERIES:
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Algebra.Com's Answer #670107 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
SUM THIS SERIES:
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document.write( "We can find all the formulas we need here:\r\n" );
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document.write( "http://godplaysdice.blogspot.com/2008/12/how-could-you-guess-formula-for-sum-of.html\r\n" );
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document.write( "The nth term is the sum of the first n cubes of the positive\r\n" );
document.write( "integers:\r\n" );
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document.write( "We look up the formula for the sum of the first n cubes of \r\n" );
document.write( "positive integers:\r\n" );
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document.write( "\"%28n%28n%2B1%29%2F2%29%5E2\"\r\n" );
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document.write( "So we are looking for this:\r\n" );
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document.write( "\"sum%28%28%28n%28n%2B1%29%2F2%29%5E2%29%2Cn=1%2C50%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"sum%28%28%28n%5E4%2B2n%5E3%2Bn%5E2%29%2F4%29%2Cn=1%2C50%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"expr%281%2F4%29sum%28%28n%5E4%2B2n%5E3%2Bn%5E2%29%2Cn=1%2C50%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"%22%22=%22%22\"\r\n" );
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document.write( "\"%22%22=%22%22\"\r\n" );
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document.write( "Now we must look up the formula for the sum\r\n" );
document.write( "of the first n 4th powers and squares of positive\r\n" );
document.write( "integers:\r\n" );
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document.write( "The sum of the first n 4th powers of positive integers is \r\n" );
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document.write( "\"%28n%282n%2B1%29%28n%2B1%29%283n%5E2%2B3n-1%29%29%2F30\"\r\n" );
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document.write( "The sum of the first n squares of powers of positive integers is \r\n" );
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document.write( "sum of the first n squares\r\n" );
document.write( " \"%28n%28n%2B1%29%282n%2B1%29%29%2F6\" \r\n" );
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document.write( "We have already looked up the formula for the sum of the first \r\n" );
document.write( "n cubes of powers of positive integers \r\n" );
document.write( "sum of the first n cubes, which again is  \r\n" );
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document.write( "\"%28n%28n%2B1%29%2F2%29%5E2\"\r\n" );
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document.write( "Substituting for the summations\r\n" );
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document.write( "\"%22%22=%22%22\"\r\n" );
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document.write( "which simplifies to\r\n" );
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document.write( "\"%28n%283n%5E4%2B15n%5E3%2B25n%5E2%2B15n%2B2%29%29%2F60\" \r\n" );
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document.write( "which actually factors as\r\n" );
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document.write( "\"%28n%28n%2B1%29%28n%2B2%29%283n%5E2%2B6n%2B1%29%29%2F60\"\r\n" );
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document.write( "although that factorization isn't necessary\r\n" );
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document.write( "Substituting n = 50 gives\r\n" );
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document.write( "17240210\r\n" );
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document.write( "Edwin
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