MathDB

2007 Guts #29: Infinite Roots of Recursive Sequence

Source:

June 22, 2012

Problem Statement

A sequence

\{a_n\}_{n\geq 1}

of positive reals is defined by the rule

a_{n+1}a_{n-1}^5=a_n^4a_{n-2}^2

for integers

n>2

together with the initial values

a_1=8

and

a_2=64

and

a_3=1024

. Compute

\sqrt{a_1+\sqrt{a_2+\sqrt{a_3+\cdots}}}