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Putnam 2008 B2

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December 8, 2008
PutnamlogarithmsintegrationlimitcalculusfactorialSupport

Problem Statement

Let F_0\equal{}\ln x. For n≥0 n\ge 0 and x>0, x>0, let \displaystyle F_{n\plus{}1}(x)\equal{}\int_0^xF_n(t)\,dt. Evaluate lim⁡n→∞n!Fn(1)ln⁡n. \displaystyle\lim_{n\to\infty}\frac{n!F_n(1)}{\ln n}.
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