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?

let x =sqrt(2+sqrt(2)....)

then x=sqrt(2+x)

x^2=2+x

x=2,-1

has to be positive so x =2!!!

Posted by red_sox_fan_032003 on 2004-02-26 21:43:43