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?

I think everyone (should) agree that if S is the solution, then S©÷-2=S.  The problem here is that there are extraneous solutions.

Of course, S can't be negative, and the negative solution must account for negative square roots.  There is another extraneous root though.  ¡Ä©÷-2=¡Ä, at least as far as I know.  I don't believe in this answer of course, but is my belief only enough proof?  I can think of ways to prove it beyond reasonable doubt, but not truly prove it, if you know what I mean.

Posted by Tristan on 2004-02-20 17:25:04