is called a p-series. In general, a p-series follows the following form:
p-series are useful because of the following theorem:
The p-series
is convergent if p > 1 and divergent otherwise.
Unfortunately, there is no simple theorem to give us the sum of a p-series. For instance, the sum of the example series is
.
If p=1, we call the resulting series the harmonic series:
By the above theorem, the harmonic series does not converge.
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