Video Transcript
Determine whether the series the
sum from 𝑛 equals one to ∞ of one over 𝑛 to the fourth power converges or
diverges.
Well, we recognise this sum to be
the form of a 𝑝-series. So we can start by writing out the
condition for convergence of a 𝑝-series. The 𝑝-series the sum from 𝑛
equals one to ∞ of one over 𝑛 to the 𝑝 power is convergent if 𝑝 is greater
than one and divergent if 𝑝 is less than or equal to one. So for this series, 𝑝 is equal to
four, which is greater than one. So we can conclude that this series
converges.
