Series Everywhere

Calculus Level 4

Define \(\large N\) as

\(\large N = \huge{ \frac{6\left(1+\frac{1}{1+3}+\frac{1}{1+3+5}+\frac{1}{1+3+5+7}+...\right)^2}{1+\frac{1}{2^4}+\frac{1}{3^4}+\frac{1}{4^4}...} }\).

If there exists a positive number \(E\) such that

\(\large E = \huge { \frac{N}{2+\frac{N}{2+\frac{N}{2+\frac{N}{2+\frac{N}{2+...}}}}}} \),

Find \(E^{2}\).

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