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$\begin{array}{ll}
\sigma(t) &= \sigma \left( \displaystyle\sum_{k=1}^{n} \dfrac{1}{k} \right) \\
&= \displaystyle\sum_{k=1}^{n+1} \dfrac{1}{k} \\
&= t + \dfrac{1}{n+1} \\
\end{array}$

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