[[Infinite series]]
# $p$-series
Given an integer $p$ the $p$-series is defined as the summation
$$
\begin{align*}
\sum_{n=1}^\infty \frac{1}{n^p}
\end{align*}
$$
In the case of $p = 1$ this is the harmonic series, which is non-convergent.
The [[Integral test]] may be used to show that a $p$-series converges iff. $p > 1$.

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