Twisted Nested Radicals!

Calculus Level 1

P=222225432\Large{P= 2 \sqrt[2]{2 \sqrt[3]{2 \sqrt[4]{2 \sqrt[5]{2 \cdots}}}} }

If P=AeBP= \large \dfrac{A^e}{B} for positive integers AA and B,B, what is A+B?A+B?

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