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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.…
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
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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MES Math Q/A stats!! 🧲🧲🧲💡💡💡
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MES Math Q/A 68: What is Faraday's Flux Rule? - YouTube - Math Q/A playlist
Faraday’s flux rule states that a changing magnetic flux through a closed circuit induces an electromotive force (emf) that opposes the change. The main difference from the more general Faraday’s law of induction is that the flux rule applies specifically to closed circuits, while the broader law describes how a changing magnetic field produces a circulating electric field even without a physical circuit.
#math #physics #science #electromagnetism #faradayslaw
Faraday’s flux rule states that a changing magnetic flux through a closed circuit induces an electromotive force (emf) that opposes the change. The main difference from the more general Faraday’s law of induction is that the flux rule applies specifically to closed circuits, while the broader law describes how a changing magnetic field produces a circulating electric field even without a physical circuit.
#math #physics #science #electromagnetism #faradayslaw
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Got the Tesla Coil to work and spark up! It also caused buzzing in my ear headphones, and got super loud and painful during the spark in my ears! I NEED a Faraday cage ASAP! ⚡️😮 • Hive
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Got the Tesla Coil to work and spark up! It also caused buzzing in my ear headphones, and got super loud and painful during the spark in my ears! I NEED a Faraday cage ASAP! ⚡️😮
• Hive
• Hive
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While I was freaking out over my Tesla coil affecting my headphones and electronics, John Hutchison was manually building 8 ft tall Tesla coils by hand! ⚡️⚡️⚡️🙌🤯 • Hive
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While I was freaking out over my Tesla coil affecting my headphones and electronics, John Hutchison was manually building 8 ft tall Tesla coils by hand! ⚡️⚡️⚡️🙌🤯
• Hive
• Hive
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The annual AI written output has exceeded that of humans, and should exceed the cumulative by 2028 😮
Big Tech is spending over 100% of its operating cash flow on capital expenditure (CAPEX), most of which is on AI infrastructure. 🤖📈 - Archive
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Fox News host Jesse Watters rockin' the Illuminati hand sign while standing on a Freemasonic checkered floor to let folks know all the gold is still in Fort Knox. 🤙👀 mes.fm/hands
This local Freemason booth has a poster with the website: ancientlight88.com
The first thing that comes to mind, of course, is the 9/11 Tribute in Light memorial, which has 88 high-powered laser lights shining into space to represent the Twin Towers. ⚡⚡🏢🏢
• Hive
The first thing that comes to mind, of course, is the 9/11 Tribute in Light memorial, which has 88 high-powered laser lights shining into space to represent the Twin Towers. ⚡⚡🏢🏢
• Hive
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MES getting ready for Canada's military draft to go fight Turpekistan or one of the other -stans in the Middle East 🔫🔫🔫🔫💣💣💣💣
US Military to begin automatic draft registration in December 2026! #WW3 😲🤡🪖🤡🇺🇸😳
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Check out my new playlist! 🗣 Bob Greenyer says the darnedest things 😹 Link - Short URL: mes.fm/bg-wildin
Bob Greenyer says steel firetrucks are made of aluminum, and downplays the significant toasted firetrucks damage.
• Firetruck with holes, crushed, warped
• BG Wildin' playlist
• Hive
• Firetruck with holes, crushed, warped
• BG Wildin' playlist
• Hive
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Bob Greenyer says steel firetrucks are made of aluminum, and downplays the significant toasted firetrucks damage. • Firetruck with holes, crushed, warped • BG Wildin' playlist • Hive
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Bob Greenyer "analyzing" MH370 cartoons vs MES analyzing MH370 cartoons.
• Hive
• BG wildin'
• MH370 psyop
• Hive
• BG wildin'
• MH370 psyop
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New Balance soccer cleats have option for "wide" shoes, first time I got cleats that actually fit my wide feet! 👟👟⚽️🙌
Got wide New Balance running shoes too! First time ever shoes fit my wide feet! 👟👟👣🙌
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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…
Example 4: Series with terms (ln n) / n diverges by the Integral Test - Hive - YouTube - Notes - Playlist - Sequences and Series
In this video, I show that the sum of the series with terms (ln n) / n diverges to infinity by computing its corresponding improper integral via the Integral Test. First noting that the natural logarithm function is continuous, and positive for x is greater than 1, then so is the corresponding function f(x) = (ln x) / x. However, it is uncertain whether the function is increasing or decreasing, so I take the derivative and show that it is negative for x is greater than the number e, thus the function itself is also decreasing. This allows us to apply the Integral Test for convergence and the corresponding improper integral approaches infinity, thus our series diverges!
#math #calculus #series #logarithms #education
In this video, I show that the sum of the series with terms (ln n) / n diverges to infinity by computing its corresponding improper integral via the Integral Test. First noting that the natural logarithm function is continuous, and positive for x is greater than 1, then so is the corresponding function f(x) = (ln x) / x. However, it is uncertain whether the function is increasing or decreasing, so I take the derivative and show that it is negative for x is greater than the number e, thus the function itself is also decreasing. This allows us to apply the Integral Test for convergence and the corresponding improper integral approaches infinity, thus our series diverges!
#math #calculus #series #logarithms #education
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