document.write( "Question 486415: sum to n terms of (1/1cube)+(1+2/1cube+2cube)+......... is \n" ); document.write( "
Algebra.Com's Answer #332760 by richard1234(7193)\"\" \"About 
You can put this solution on YOUR website!
Use the fact that\r
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\n" ); document.write( "\n" ); document.write( " Since the sum of the first i positive integers is i(i+1)/2, we reciprocate so our sum is equal to\r
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\n" ); document.write( "\n" ); document.write( "I learned a nice Mathcounts trick that you can decompose that fraction to 1/i - 1/(i+1) (if you don't know it, just decompose it normally using partial fractions). This becomes a \"telescoping\" sum where all the terms collapse except the first and last:\r
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