Given the integer and the real number determine the maximum of taken over all nonnegative numbers with sum
%V0
Given the integer $n > 1$ and the real number $a > 0$ determine the maximum of $\sum_{i=1}^{n-1} x_i x_{i+1}$ taken over all nonnegative numbers $x_i$ with sum $a.$
Izvor: Međunarodna matematička olimpijada, shortlist 1979
Školjka 
and the real number 
determine the maximum of 
taken over all nonnegative numbers 
with sum 