MathDB

Let

n\geq 2

be an integer. Let

a_{ij}, \ i,j=1,2,\ldots,n

n^2

positive real numbers satisfying the following conditions:
[*]For all

i=1,\ldots,n

we have

a_{ii}=1

and, [*]For all

j=2,\ldots,n

the numbers

a_{ij}, \ i=1,\ldots, j-1

form a permutation of

1/a_{ji}, \ i=1,\ldots, j-1.

Given that

S_i=a_{i1}+\cdots+a_{in}

, determine the maximum value of the sum

1/S_1+\cdots+1/S_n.

Problem Statement