# 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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