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?

(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