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Source: 1984 National High School Mathematics League, Exam Two, Problem 4

February 22, 2020

Problem Statement

Define ana_n: the last digit of 12+22+32+⋯+n21^2+2^2+3^2+\cdots+n^2. Prove that 0.a1a2a3⋯‾\overline{0.a_1 a_2 a_3 \cdots} is a rational number.
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