Video: Using the Net Change Theorem

Determine whether the series ∑_(𝑛 = 1)^(∞) 1/𝑛⁴ converges or diverges.

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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.

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