Assistance with an infinetly nested radical

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SUMMARY

The discussion centers on the convergence of an infinitely nested radical. Participants confirm that the nested radical converges to a specific value, although determining this limit analytically presents challenges. Recursive function methods were attempted but did not yield the desired results. The conversation emphasizes the need for comparative analysis with known convergent nested radicals to establish proof of convergence.

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fedaykin
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Hello, and thank you for any assistance offered.

I believe the attached nested radical to converge to a value, but I can't find what it is. I've tried the typical recursive function methods to no luck.
 

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I believe the attached nested radical to converge to a value
Yes, it converges. To prove it, we compare it to a convergent nested radical.
But the anylitical computation of the limit value is a challenge.
 

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