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?

If S=√(2+√(2+√(2+...)) then S²=2+S, which can be solved giving S=2.

If 2 was replaced with X, then the equation would be S²=X+S, and S would be (1+√(1+4X))/2

Posted by Federico Kereki on 2004-02-20 08:47:53