Given that:

F_m(x) = √(2 - √(2 + √(2 + √(2 + .....√(2 + √x))))) (m square roots)

Evaluate this limit:

Limit   F_m(2)/F_m(3)
m → ∞

that both the numerator and denominator approach 2/(1+sqrt(5)) = 1/phi ~= .6180339887498948, so that the fraction approaches 1. (wrong; see below)

(Sorry; misunderstood function -- the signs don't alternate as assumed below)

All the 2's in the function predominate over the lone 3, when 3 is used.

DEFDBL A-Z
x = 3
f = SQR(x)
DO
  f = SQR(2 + f)
  f = SQR(2 - f)
  PRINT f
LOOP

 

Edited on November 26, 2009, 1:44 pm

Posted by Charlie on 2009-11-26 13:37:09