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2015 China South East MO Grade 11 P2

Source: 2015 China South East MO Grade 11 P2

January 16, 2018

inequalitiesalgebra

Problem Statement

Given a sequence

\{ a_n\}_{n\in \mathbb{Z}^+}

defined by

a_1=1

and

a_{2k}=a_{2k-1}+a_k,a_{2k+1}=a_{2k}

for all positive integer

k

. Prove that, for any positive integer

n

,

a_{2^n}>2^{\frac{n^2}{4}}

.

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