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Exercise 2: Sum of diameters of Infinite Circles - Hive - YouTube - Notes - Playlist - Sequences and Series In this video, I show that the sum of diameters of an infinite number of circles contacting between two big circles sums to the radius of the biggerโ€ฆ
Introduction to the Integral Test and Estimating Sums of Infinite Series - Hive - YouTube - Notes - Playlist - Sequences and Series

In this video, I go over an introduction into estimating sums of series by examining whether their corresponding improper integrals converge or diverge, thus providing the basis for the Integral Test. Often times, there is no exact formula for the sum of a series, so we need to obtain ways of estimating their sums.

#math #calculus #series #integral #education
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7 hours of FEMA Kurt Sonnenfeld 9/11 Ground Zero footage - Hive
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Rare FEMA footage and angle of the tiny stub of Building 3 and the still-standing exterior lobby columns of the South Tower. ๐Ÿ˜ฎ

โ€ข Hive
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Introduction to the Integral Test and Estimating Sums of Infinite Series - Hive - YouTube - Notes - Playlist - Sequences and Series In this video, I go over an introduction into estimating sums of series by examining whether their corresponding improper integralsโ€ฆ
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/(nยฒ+1), which converges since its improper integral converges and equals ฯ€/4.

#math #calculus #series #integral #trigonometry
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Here is another squirrel ๐Ÿฅณ
Squirrel won't let me pass ๐Ÿฟ๐Ÿšท๐Ÿ˜ฎ
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Drone starting forest fires woww ๐Ÿ‘€
Huge forest fire smoke dimming the Sun wow ๐ŸŒณ๐ŸŒณ๐ŸŒฒ๐ŸŽ„๐ŸŒด๐Ÿ”ฅ๐Ÿ”ฅ๐Ÿ”ฅ๐Ÿ”ฅ๐Ÿ˜ถโ€๐ŸŒซ๏ธ๐Ÿ’จ๐ŸŒค๐ŸŒฅ
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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.โ€ฆ
The p-Series โˆ‘ 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
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