If P is defined as $$P = 2\sqrt[2]{2\sqrt[3]{2\sqrt[4]{2\sqrt[5]{2...}}}}$$ And if $$P = \frac {A^e}{B}$$ for positive integers A and B, what is A and B?
2026-03-30 10:07:29.1774865249
Progressive Nested Radicals
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Hint: $$P = 2\sqrt[2]{2\sqrt[3]{2\sqrt[4]{2\sqrt[5]{2...}}}}=2^1\cdot 2^{\frac {1}{2!}}\cdot 2^{\frac{1}{3!}}\cdots=2^{1+\frac{1}{2!}+\frac{1}{3!}+\cdots}$$