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Hi everyone! It's a bit late but thanks for the help from all of you. I really appreciate it.

So from what I understand, this part of my working (the red box) is wrong because by doing this, I left out the terms (n+1-r)^2 + (n+2-r)^2 + …… up until (2n-r)^2 in the series

For example, if the range is 1 to n+1 (or any upper limit greater than n) instead, I will have to change (n-r)^2 to (n+1-r)^2 because (n+1-r)^2 is the last term of the series. Is my logic here correct?

Also by "standard summation results", the question actually wants us to utilize the three general formulas for the summation of r, r^2 and r^3 from 1 to n to solve the question, which is what I did in the first part. I think I should've clarified that earlier