IMO 1970 LL CZS19

Origin: CZS

Problem

Let n > 1 be a natural number, a \geq1 a real number, and x1, x2, . . . , xn numbers such that x1 = 1, xk+1 xk = a+\alphak for k = 1, 2, . . . , n− 1, where \alphak are real numbers with \alphak \leq k(k+1). Prove that n−1\sqrtxn < a + n −1.