Summations

$\sum_{j \neq k}^{N} x = N^2, \ \ \ \ j=1,k=1$

What is $x$?

I thought it would be 1, but does this not give the answer $N^2-N$?

Yep, because of the $j \neq k$ condition. Is x allowed to depend on N? If it is, then there's a simple tweak you can do (it helps me to visualise an NxN matrix, where the required quantity is the sum of all the entries, and where the diagonal entries are 0).

Yep, x can depend on N. Is $x = \frac{N^2}{N^2-N} =\frac{N}{N-1}$??

Yep, exactly - then each row of the matrix adds up to N, and there are N rows, so the whole thing comes to N^2.

Thanks, what a wonderfully easy way to think about it, I shall never have an issue like this again now!