Question about a nested radical identity of Ramanujan involving $\sqrt 5$

Asked Oct 09 '13 at 22:00

Active Jan 06 '14 at 15:29

Viewed 123 times

Ramanujan stated this radical in his lost notebook:

$$\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$$

Where the pattern of the signs is $++-+++-++++-+++++-\cdots$

I do not have access to his lost notebook. I wonder how we can prove this.

For periodic sign changes this kind of question is easy but for nonperiodic Im clueless.

edited Jan 06 '14 at 15:29

Grigory M

asked Oct 09 '13 at 22:00

mick

Is this different than: http://math.stackexchange.com/questions/515253/how-to-prove-sqrt5-sqrt5-sqrt5-sqrt5-sqrt5-sqrt5-sqrt5-dots ? – Scott H. Oct 09 '13 at 22:19
Is cocopuffs right or not ? – mick Oct 09 '13 at 22:25
I have no idea. – Scott H. Oct 09 '13 at 22:55

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