# A tangled nest we weave

Calculus Level 5

$\Large S = \displaystyle\sqrt{\pi \sqrt[3]{e \sqrt[4]{\pi \sqrt[5]{e \sqrt[6]{\pi \sqrt[7]{e \sqrt[8]{\pi \cdots}}}}}}}$

Find the value of $$\lfloor 1000*S \rfloor$$.

Clarification: The small numbers $$3, 4,5,\ldots$$ indicate the $$n^\text{th}$$ roots and are not powers.

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