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a_n =(\sqrt3 +\sqrt2)^{2n}, b_n=a_n +1/a_n

Source: China Northern MO 2011 p1 CNMO

May 4, 2024

algebrarecurrence relationSequence

Problem Statement

It is known that the general term

\{a_n\}

of the sequence is

a_n =(\sqrt3 +\sqrt2)^{2n}

(

n \in N*

), let

b_n= a_n +\frac{1}{a_n}

. (1) Find the recurrence relation between

b_{n+2}

,

b_{n+1}

,

b_n

. (2) Find the unit digit of the integer part of

a_{2011}

.

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