1

Part of 2024 China Second Round

Problems(1)

the nearest distance in geometric sequence

Source: 2024 China High School Olympics A P1

A positive integer

r

is given, find the largest real number

C

such that there exists a geometric sequence

\{ a_n \}_{n\ge 1}

with common ratio

r

\| a_n \| \ge C

for all positive integers

n

\| x \|

denotes the distance from the real number

x

to the nearest integer.

algebraSequence