Question Video: Using the Net Change Theorem Mathematics • Higher Education

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.