SOLUTION: Calculate the sum: 1/4(1^3) + 1/9((1^3) + (2^3)) + 1/16((1^3) + (2^3) + (3^3)) +...+ 1/2704((1^3) + (2^3) + (3^3) +...+ (51^3))

Question 1191490: Calculate the sum:
1/4(1^3) + 1/9((1^3) + (2^3)) + 1/16((1^3) + (2^3) + (3^3)) +...+ 1/2704((1^3) + (2^3) + (3^3) +...+ (51^3))
Answer by greenestamps(13334) (Show Source): You can put this solution on YOUR website!

The fractional part of the n-th term is

The other factor in the n-th term is the sum of the cubes of the first n integers:

So the nth term in the sequence is

There are 51 terms in the sequence, so the sum is

Use the formula for the sum of the first n squares to get the final answer.

ANSWER: 22763/4

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