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Rooting For The Limit II (Posted on 2009-11-26) Difficulty: 3 of 5
Given that:

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

Evaluate this limit:

Limit   Fm(2)/Fm(3)
m → ∞

See The Solution Submitted by K Sengupta    
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Some Thoughts It would seem... | Comment 1 of 4

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

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