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TOT 2006 Fall - Senior A-Level p3 integer part of n\sqrt2, irrational

Source:

February 25, 2020
Integer PartalgebraDigitirrational

Problem Statement

The nn-th digit of number a=0.12457...a = 0.12457... equals the first digit of the integer part of the number n2n\sqrt2. Prove that aa is irrational number. (6)