# Recurring Styles #15 - Continued Product!

Calculus Level 5

$\Large{L = \lim_{n \to \infty} \dfrac{ \left| a_{n+1} - a_n \right| }{\sqrt{n}}}$

Let $$\{ a_n \}$$ be a sequence such that $$a_1=1, \ a_n a_{n+1} = n$$ for every $$n \in \mathbb Z^+$$. If $$L$$ can be expressed as:

$\large{ \sqrt{\dfrac{\pi^A}{B}} - \sqrt{C\pi^D}}$

where $$A,B,C,D \in \mathbb Z$$, submit the value of $$ABCD$$ as your answer.

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