6

Part of 2012 Ukraine Team Selection Test

Problems(1)

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

Source: Ukraine TST 2012 p6

For the positive integer

k

we denote by the

a_n

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

irrational numberirrationalDigitsdecimal representationalgebra