I have this matrix. It is a Gram matrix of some bilinear form on the R^n.

Question

(1 1/2 1/3 1/4 ... 1/(n-1) 1/n) (1/2 1/3 1/4 1/5 ... 1/n 1/(n+1)) (1/3 1/4 1/5 1/6 ... 1/(n+1) 1/(n+2)) (1/4 1/5 1/6 1/7 ... 1/(n+2) 1/(n+3)) (...................................) (1/(n-3) 1/(n-2) 1/(n-1) 1/n ... 1/(2n-5) 1/(2n-4)) (1/(n-2) 1/(n-1) 1/n 1/(n+1) ... 1/(2n-4) 1/(2n-3)) (1/(n-1) 1/n 1/(n+1) 1/(n+2) ... 1/(2n-3) 1/(2n-2)) (1/n 1/(n+1) 1/(n+2) 1/(n+3) ... 1/(2n-2) 1/(2n-1))

I need to prove that it is positive. But I can't complete it.