IMO 1987 LL GBR27

Origin: GBR

Problem

Find, with proof, the smallest real number C with the following property: For every infinite sequence {xi} of positive real numbers such that x1 + x2 + \cdot \cdot \cdot + xn \leqxn+1 for n = 1, 2, 3, . . ., we have \sqrtx1 + \sqrtx2 + \cdot \cdot \cdot + \sqrtxn \leqc\sqrtx1 + x2 + \cdot \cdot \cdot + xn for n = 1, 2, 3, . . ..