Radicals Overload

Calculus Level 3

22222543=? \large 2 \displaystyle\sqrt{2\sqrt[3]{2 \sqrt[4]{2 \sqrt[5]{2 \cdots}}}} = \,?

Clarification: e=limn(1+1n)n2.718\displaystyle e = \lim_{n\to\infty} \left(1 + \dfrac1n\right)^n \approx 2.718 .

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