Just a long problem

Calculus Level pending

Define \(x\) and \(y\) as

\(\huge x = \sum _{n=1}^{\infty }\left(\frac{1}{\sum _{k=1}^n\left(k\right)}\right) \)

\( \huge y = \sum _{n=1}^{\infty }\left(\frac{1}{\sum _{k=1}^n\left(2k-1\right)}\right) \)

If there exists a number \(z\), such that

\(\huge z = \frac {xy}{\pi^{2}} \)

Then find the exact positive value of

\( \sqrt{z+2z\sqrt{z+2z\sqrt{z+2z\sqrt{z+2z\sqrt{z+...}}}}} \)

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