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Calculate the determinant of $A_{n\times n}=((a_{ij})_{1\le i\le n})_{1\le j\le n}$ where

$$a_{ij}=\frac{1}{i+j-1}$$

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Thanks @DominicMichaelis for pointing out the typo. –  Abhra Abir Kundu Mar 1 '13 at 13:45
    
@AbhraAbirKundu: of course you mean for square matrices as DM notes. Hint, try a 2x2, 3x3 and look for a pattern to generalize. –  Amzoti Mar 1 '13 at 13:48
    
Did you try anything? My first idea would be calculating for small $n$ and try to find a system –  Dominic Michaelis Mar 1 '13 at 13:49
    
Yes i did try for small $n$ like $n=2,3,4$ but couldn't find any pattern in those determinants. –  Abhra Abir Kundu Mar 1 '13 at 13:52

1 Answer 1

This matrix is known as Hilbert Matrix, see here: http://en.wikipedia.org/wiki/Hilbert_matrix

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Thanks @pritam for the resource. –  Abhra Abir Kundu Mar 1 '13 at 13:56
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@Abhra Abir Kundu: You are welcome, once you know the formula you can try to prove it by induction. –  pritam Mar 1 '13 at 14:06

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