Assistance with an infinetly nested radical

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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Mathematics news on Phys.org
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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  • Nested radical.JPG
    Nested radical.JPG
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