Problem

Source: Bundeswettbewerb Mathematik 2019, Round 1 - Problem 4

Tags: Digits, sqrt, number theory



In the decimal expansion of $\sqrt{2}=1.4142\dots$, Isabelle finds a sequence of $k$ successive zeroes where $k$ is a positive integer. Show that the first zero of this sequence can occur no earlier than at the $k$-th position after the decimal point.