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     \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?
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    (Original post by adie_raz)
     \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).
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    (Original post by Smaug123)
    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} ??
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    (Original post by adie_raz)
    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.
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    (Original post by Smaug123)
    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!
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    (Original post by adie_raz)
    Thanks, what a wonderfully easy way to think about it, I shall never have an issue like this again now!
    No problem it doesn't work so well for things like the sum of 1/x, because it's not so clear what each row sums to, but for constants it can be a simpler way. (Makes use of the innate ability to picture things and work with concrete objects, I suppose, much like the way I do Bayes's Law with a kind of Carroll diagram.)
 
 
 
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