As easy as pie

Calculus Level 2

\[\large \begin{eqnarray} A&=&\frac{4}{1+\frac{1^2}{3+\frac{2^2}{5+\frac{3^2}{7+\frac{4^2}{9+\cdots}}}}} \\ B&=&\frac{2}{\frac{\sqrt{2}}{2}\times\frac{\sqrt{2+\sqrt{2}}}{2}\times\frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2}\times\cdots} \\ C&=&\ 4-\dfrac{4}{3}+\dfrac{4}{5}-\dfrac{4}{7}+\dfrac{4}{9}-\cdots\\ D&=&\ 3+\dfrac{4}{2\times3\times4}-\dfrac{4}{4\times5\times6}+\dfrac{4}{6\times7\times8}-\dfrac{4}{8\times9\times10}+\cdots\end{eqnarray}\]

Which option/s is/are equal to \(\pi\)?

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