p-series Test
For the the series in form of 1/nᴾ, the easiest way to determine its convergence is using the p-series test:

▼Refer to xaktly: p-series test/harmonic series 
Harmonic Series
Harmonic SeriesHarmonic Series is
∑ 1/n, and Harmonic Series DIVERGES. That's all you need to know.

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