is there a way to express any given root of an integer in a continued fraction? i.e. Sqrt[2] = 1 + 1/(2 + Sqrt[2] - 1) and the process can be continued infinitely to get a fraction that defines the radical with only integers.(adsbygoogle = window.adsbygoogle || []).push({});

so my question is can this kind of thing be done with any square root? any integer root?

next question is is there a way to determine the limit of the following:

Sqrt[x^0*a+Sqrt[x*a+Sqrt[x^2*a+Sqrt[x^3*a...]]]] or a similar form for a progression of numbers?

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# Continued fractions and nested radicals

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