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Prove sequence is bounded

Source: Japan TST 2017 P8

January 24, 2021

algebraSequenceinequalities

Problem Statement

A sequence of positive integers

a_1,a_2,\ldots

satisfies

a_n > \frac{a_{n+1}+a_{n+2}+\ldots +a_{2n}}{n+2016}

for all positive integers

n

. Show that there exists a positive real

C

such that

a_n<C

for all positive integers

n

.

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