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Putnam 1981 A1

Source: Putnam 1981

March 31, 2022
PutnamConvergence

Problem Statement

Let E(n)E(n) denote the largest integer kk such that 5k5^k divides 11⋅22⋅33⋅…⋅nn.1^{1}\cdot 2^{2} \cdot 3^{3} \cdot \ldots \cdot n^{n}. Calculate lim⁡n→∞E(n)n2.\lim_{n\to \infty} \frac{E(n)}{n^2 }.
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