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August 20, 2014

August 20, 2014

Posted by **Hannah** on Tuesday, July 7, 2009 at 8:15am.

- Math -
**Reiny**, Tuesday, July 7, 2009 at 9:10amA(n) = √(3 + √(3 + √(3 + ...))..) to infinity

let x = √(3 + √(3 + √(3 + ...))..)

square both sides

x^2 = 3 + √(3 + √(3 + √(3 + ...))..)

or

x^2 = 3 + x

x^2 - x - 3 = 0

by the formula

x = (1+√13)/2

= appr. 2.302775638... which I got by repeatedly doing the following on my calculator about 20 times

1. √3

2. =

3. +3

4. =

5. √

goto 2.

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