The Integral Test + Example on Convergence of a Series - Hive - YouTube - Notes - Playlist - Sequences and Series

In this video, I go over the Integral Test, which states that a series converges only if its corresponding improper integral also converges. Likewise, if the improper integral diverges, then the series also diverges. This stems from my earlier introduction video illustrating how the sum of an infinite series is directly tied to the area under the curve of the equation for the terms of the series. I illustrate this with an example on the series with terms 1/(n²+1), which converges since its improper integral converges and equals π/4.

#math #calculus #series #integral #trigonometry

In Michael Jordan's first 3-peat NBA championships, he capped off the 1993 NBA Finals in Game 6 with 33 points on June 20.

33 days later on July 23, his father James was murdered... 👀

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Squirrel won't let me pass 🐿🚷😮

Chris Shak made VIP tickets to the 9/11 Museum Livestream this Saturday at 1 PM PST!

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The p-Series ∑ 1/n^p is convergent if p is greater than 1 - Hive - YouTube - Notes - Playlist - Sequences and Series

In this video, I use the Integral Test to show that the p-series, whose terms are 1/n^p, is convergent if p is greater than 1 and divergent for all other values of p. When p is less than 0, the terms approach infinity; when p = 0, the terms equal 1, hence it is divergent by the test for divergence; and when p = 1, we get the harmonic series, which is also divergent. I also illustrate this with examples on a convergent and a divergent p-series. Note also that when using the Integral Test, the corresponding improper integrals do NOT, in general, equal the sum of the series.

#math #calculus #series #pseries #education

Forest Fire smoke got the Sun lookin' like a Blood Moon 🌤🎴👀