I couldn't get farther than this:
an = an-1+
(1+an-12) >2 an-1 > 22an-2>...>2n-1a1
Also, an <2an-1+1<22an-2+2+1<...<2n-1a1+2n-2+..+1
Hence a1<an/2n-1<a1+1/2+1/22+...+1/2n-1.
as n
inf, by Sandwich Theorem, the required limit lies between a1 and a1+1 i.e. between 1 and 2.
Moderation Team
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