Induction Time

Algebra Level 4

Denote $$S_k$$ as the sum of infinite series with first term $$k$$ and common ratio $$\frac {1}{k+1}$$. State the expression below in terms of $$n$$.

$S_1 ^2 + S_2 ^2+S_3 ^2 + \ldots + S_{2n-1} ^2$

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