# 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 \(n\).

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

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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