Let's do some calculus! (38)

$\begin{aligned} S_1 &=& \dfrac 34 \displaystyle \sum_{n=1}^{\infty} \dfrac{1}{n^2} \\ S_2 &=& \displaystyle \sum_{n=0}^{\infty} \dfrac{1}{{(1+2n)}^2} \\ S_3 &=& -\dfrac 32 \displaystyle \sum_{n=1}^{\infty} \dfrac{{(-1)}^n}{n^2} \\ S_4 &=& 2 {\left( \displaystyle \sum_{n=0}^{\infty} \dfrac{{(-1)}^n}{1+2n} \right)}^2 \end{aligned}$

Choose the correct order of the infinite sums listed above.

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