$𝑝$ -series

Given an integer $𝑝$ the $𝑝$ -series is defined as the summation

\infty \sum 𝑛 = 1 1 𝑛 𝑝

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. $𝑝 > 1$ .

#state/tidy | #SemBr

𝑝-series

$𝑝$ -series