IMO 1983 LL LUX46

Let f be a real-valued function defined on I = (0, +\infty) and

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IMO 1983 LL LUX46

Origin: LUX

Problem

Let f be a real-valued function defined on I = (0, +\infty) and having no zeros on I. Suppose that lim x\to+\infty f ′(x) f(x) = +\infty. For the sequence un = ln f(n+1) f(n) , prove that un \to+\infty(n \to+\infty).