MathDB

max M, a_{n+1}/a_n >M if a_0+a_1+...+a_{n-1} >= 3 a_n - a_{n+1}

Source: 2022 Greece TST p3

November 3, 2022

algebrainequalitiesSequence

Problem Statement

Find largest possible constant

M

such that, for any sequence

a_n

n=0,1,2,...

of real numbers, that satisfies the conditions : i)

a_0=1

a_1=3

ii)

a_0+a_1+...+a_{n-1} \ge 3 a_n - a_{n+1}

for any integer

n\ge 1

to be true that

\frac{a_{n+1}}{a_n} >M

for any integer

n\ge 0