SOLUTION: sum to n terms of (1/1cube)+(1+2/1cube+2cube)+......... is

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Question 486415: sum to n terms of (1/1cube)+(1+2/1cube+2cube)+......... is
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Use the fact that

Since the sum of the first i positive integers is i(i+1)/2, we reciprocate so our sum is equal to



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:

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