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Power to the 2 (Posted on 2004-02-20) Difficulty: 2 of 5
What is the limit to this sequence?

√(2)
√(2+√(2))
√(2+√(2+√(2)))
√(2+√(2+√(2+√(2))))...

In general, what is the sequence in terms of x if 2 is replaced with x?

See The Solution Submitted by Gamer    
Rating: 2.8750 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 8 of 10 |
(In reply to Solution by Larry)

Before equating S^2 to 2+S we must first prove that the limit exists.  This can be done, for example, by showing that the sequence is increasing and bounded above.  The existence of the limit would then follow from the monotone convergence theorem.
  Posted by Nick Hobson on 2004-02-23 14:02:27

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