1I ' ll just say a few things ............
1 . 
2 . 
3 . 
I think these suffice .
Let 0 < a ≤ b. Define
a1 = a+b2, b1 = √a1 b
and for each integer k≥1,
ak+1 = ak + bk 2, bk+1 = √ak+1 bk .
Find the limit of the sequence {bn}. That is find
\lim_{n\to\infty} b_n
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4 Answers
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341http://www.goiit.com/posts/listByUser/1920/5929.htm
I would like to emphasize what the author of the book from where I filched that solution had to say :"By the way, this is a hard problem by any competition standard"
66Well, at least I think otherwise. Definitely this problem is not suitable for the engineering entrances. But its not that hard.