What is the value of $\sqrt{x + \sqrt{ x + \sqrt{ x + \cdots } } }\,$? I know the basic trick to calculate this using $f = \sqrt{ x + f }$. But, I want more accurate answer which is I am not getting with this formula.
Asked
Active
Viewed 1,933 times
2 Answers
5
Squaring we get $f^2=x+f\iff f^2-f-x=0\implies f=\dfrac{1\pm\sqrt{1+4x}}2$
Now as $f>0,$ discard the negative root assuming $x>0$
lab bhattacharjee
- 274,582
-
2Reaching 100k! Congrats! – Jack D'Aurizio Sep 20 '14 at 04:46
-
@JackD'Aurizio, Thanks. How to discard $$\frac{1-\sqrt{1+4x}}2$$ if $x<0$? – lab bhattacharjee Sep 20 '14 at 04:50
-
Hey lab ! Congratulations – Claude Leibovici Sep 20 '14 at 04:58
-
@ClaudeLeibovici, Thanks. Could you please have another look into http://math.stackexchange.com/questions/938585/integral-with-quadratic-square-root-inside-trigonometric-functions/938589#938589 ? – lab bhattacharjee Sep 20 '14 at 05:01
-
I did but may I confess that I do not see how you finish ! – Claude Leibovici Sep 20 '14 at 05:09
