Given that $$\{a_n\}$$ is a sequence of real numbers such that the limit, $$\displaystyle \lim_{n\to\infty} \dfrac{\ln a_n}{2^n}$$ exists.

Prove that the following infinitely nested functions also converges.

$\displaystyle \sqrt{a_{1} + \sqrt{a_{2} + \ldots + \sqrt{a_{n}}}}$

This is a part of the set Formidable Series and Integrals

Note by Ishan Singh
2 years, 1 month ago

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