Ink on Sequences #5

Calculus Level 4

A sequence \(\{a_n\}\) is an arithmetic progression.

Given that \(a_{2016}=\sqrt{2016}\) and \(a_{2017}=\sqrt{2017},\) find the value of:

\[\large \lim_{n\to\infty} \dfrac{\left(\sqrt{a_2+a_4+a_6+~\cdots~+a_{2n}}-\sqrt{a_1+a_3+a_5+~\cdots~+a_{2n-1}}\right)^2}{\sqrt{2017}-\sqrt{2016}}\]


This problem is a part of <Inconsequences!> series.

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