MathDB

irrational number, by left digits in decimal notation of 2^n

Source: Ukraine TST 2012 p6

April 29, 2020

irrational numberirrationalDigitsdecimal representationalgebra

Problem Statement

For the positive integer

k

we denote by the

a_n

, the

k

from the left digit in the decimal notation of the number

2^n

(

a_n = 0

if in the notation of the number

2^n

less than the digits). Consider the infinite decimal fraction

a = \overline{0, a_1a_2a_3...}

. Prove that the number

a

is irrational.