MathDB

Show that

r = 2

is the largest real number

r

which satisfies the following condition:
If a sequence

a_1

a_2

\ldots

of positive integers fulfills the inequalities

a_n \leq a_{n+2} \leq\sqrt{a_n^2+ra_{n+1}}

for every positive integer

n

, then there exists a positive integer

M

such that

a_{n+2} = a_n

for every

n \geq M

Problem Statement