document.write( "Question 174497: find the sum of following series:
\n" ); document.write( " n*1+(n-1)*2+(n-2)*3+.........+n*1 \n" ); document.write( "
Algebra.Com's Answer #129517 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"sum%28+matrix%281%2C4%2C+%22%22%2C+%22%5B%22%2C+n-%28k-1%29%2C%22%5D%2Ak%22+%29%2Ck=1%2Cn%29\" =\r\n" );
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document.write( "\"sum%28+matrix%281%2C2%2C+%22%22%2C+%28n-k%2B1%29k+%29%2Ck=1%2Cn%29\" =\r\n" );
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document.write( "\"sum%28+matrix%281%2C2%2C+%22%22%2C+nk-k%5E2%2Bk+%29%2Ck=1%2Cn%29\" =\r\n" );
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document.write( "Combine the 1st and 3rd terms\r\n" );
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document.write( "The first sum is the arithmetic series of the first n positive\r\n" );
document.write( "integers,\r\n" );
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document.write( "which is given by the formula: \"%28n%28n%2B1%29%29%2F2\"\r\n" );
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document.write( "so we have\r\n" );
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document.write( "The remaining sum is the sum of the squares of the first n\r\n" );
document.write( "positive integers.  This is also a well-known formula:\r\n" );
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document.write( "\"%28n%28n%2B1%29%282n%2B1%29%29%2F6\"\r\n" );
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document.write( "So now we have:\r\n" );
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document.write( "\"%28n%2B1%29%28%28n%28n%2B1%29%29%2F2%29+-+%28n%28n%2B1%29%282n%2B1%29%29%2F6\"\r\n" );
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document.write( "Rewrite the second term:\r\n" );
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document.write( "\"%28n%2B1%29%28%28n%28n%2B1%29%29%2F2%29+-+%28n%28n%2B1%29%2F2%29%28%282n%2B1%29%2F3%29\"\r\n" );
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document.write( "Factor out \"%28n%28n%2B1%29%29%2F2\"\r\n" );
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document.write( "\"%28%28n%28n%2B1%29%29%2F2%29%28%28n%2B1%29-%282n%2B1%29%2F3%29\" \r\n" );
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document.write( "Get LCD in the right parentheses:\r\n" );
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document.write( "\"%28%28n%28n%2B1%29%29%2F2%29%283%28n%2B1%29%2F3-%282n%2B1%29%2F3%29\"\r\n" );
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document.write( "\"%28%28n%28n%2B1%29%29%2F2%29%28%283n%2B3%29%2F3-%282n%2B1%29%2F3%29\"\r\n" );
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document.write( "\"%28%28n%28n%2B1%29%29%2F2%29%28%283n%2B3-%282n%2B1%29%29%2F3%29%29\"\r\n" );
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document.write( "\"%28%28n%28n%2B1%29%29%2F2%29%28%283n%2B3-2n-1%29%2F3%29%29\"\r\n" );
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document.write( "\"%28%28n%28n%2B1%29%29%2F2%29%28%28n%2B2%29%2F3%29%29\"\r\n" );
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document.write( "\"%28n%2A%28n%2B1%29%28n%2B2%29%29%2F6\"\r\n" );
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document.write( "Edwin
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