Mathematical series | Articles containing proofs | Theorems about prime numbers
The sum of the reciprocals of all prime numbers diverges; that is: This was proved by Leonhard Euler in 1737, and strengthens Euclid's 3rd-century-BC result that there are infinitely many prime numbers and Nicole Oresme's 14th-century proof of the divergence of the sum of the reciprocals of the integers (harmonic series). There are a variety of proofs of Euler's result, including a lower bound for the partial sums stating that for all natural numbers n. The double natural logarithm (log log) indicates that the divergence might be very slow, which is indeed the case. See Meissel–Mertens constant. (Wikipedia).
MegaFavNumbers - 73,496,969,437, palindromic primes, programming squares
Some properties of the number 73,496,969,437. Links and details below: Comment thread from James Grime's video (amicable numbers conjecture): https://www.youtube.com/watch?v=R2eQVqdUQLI Matt Parker's tangent video (biggest tangent of a prime): https://www.youtube.com/watch?v=A7eJb8n8zAw
From playlist MegaFavNumbers
How to find the zeros of a polynomial using the sum of two cubes
👉 Learn how to find the zeroes of a polynomial equation/expression involving the sum/difference of two cubes. Given a polynomial having the sum of two cubes, the polynomial can be factored as follows: a^3 + b^3 = (a + b)(a^2 - ab + b^2). Similarly, given a polynomial having the difference
From playlist Zeros of a Polynomial by Factoring
Learn how to find the all the zeros of a polynomial with sum of two cubes
👉 Learn how to find the zeroes of a polynomial equation/expression involving the sum/difference of two cubes. Given a polynomial having the sum of two cubes, the polynomial can be factored as follows: a^3 + b^3 = (a + b)(a^2 - ab + b^2). Similarly, given a polynomial having the difference
From playlist Zeros of a Polynomial by Factoring
What is the multiplicity of a zero?
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Euler-Mascheroni III: Another NUCLEAR proof of the infinitude of primes
Follow the channel's Instagram: @whatthehectogon https://www.instagram.com/whatthehect... Check out these channels! Marching West (a DnD channel run by my friend Bill) https://www.youtube.com/channel/UCFNd... Twitter: @WestMarching https://twitter.com/WestMarching Instagram: @marchingwes
From playlist Analysis
Euler-Mascheroni V: The Meissel-Mertens Constant
Channel social media: Instagram: @whatthehectogon https://www.instagram.com/whatthehectogon/ Twitter: @whatthehectogon https://twitter.com/whatthehectogon Check out my friend Bill's DnD channel: Marching West https://www.youtube.com/channel/UCFNd... Associated social media: Twitter: @Wes
From playlist Analysis
The Reciprocal Prime Series (this proof should be taught in calculus!)
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From playlist Cool Math Series
Euler-Mascheroni II: a NUCLEAR proof on the infinitude of primes
Follow the channel's Instagram: @whatthehectogon https://www.instagram.com/whatthehect... Check out these channels! Marching West (a DnD channel run by my friend Bill) https://www.youtube.com/channel/UCFNd... Twitter: @WestMarching https://twitter.com/WestMarching Instagram: @marchingwes
From playlist Analysis
Euler-Mascheroni I: Three proofs that the Harmonic Series diverges!
Follow the channel's Instagram: @whatthehectogon https://www.instagram.com/whatthehect... Check out these channels! Marching West (a DnD channel run by my friend Bill) https://www.youtube.com/channel/UCFNdEg2zs7l5di7astgNmWA Twitter: @WestMarching https://twitter.com/WestMarching Instagr
From playlist Analysis
Learn how and why multiplicity of a zero make sense
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Solve and write the linear factorization using the sum of two cubes
👉 Learn how to find the zeroes of a polynomial equation/expression involving the sum/difference of two cubes. Given a polynomial having the sum of two cubes, the polynomial can be factored as follows: a^3 + b^3 = (a + b)(a^2 - ab + b^2). Similarly, given a polynomial having the difference
From playlist Zeros of a Polynomial by Factoring
Find the zeros factoring vs square root method
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Prime Reciprocal Series with @blackpenredpen (Oxford Maths Interview Question)
Steve from blackpenredpen answers a real Oxford University maths admissions interview question set by Oxford Mathematician (and interviewing tutor) Dr Tom Crawford. The question looks at the divergence of the sum of the reciprocals of the prime numbers, using the Fundamental Theorem of A
From playlist Interviews
What do the zeros roots tell us of a polynomial
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. This course is about calculus 2
From playlist Calculus
700 years of secrets of the Sum of Sums (paradoxical harmonic series)
Today's video is about the harmonic series 1+1/2+1/3+... . Apart from all the usual bits (done right and animated :) I've included a lot of the amazing properties of this prototypical infinite series that hardly anybody knows about. Enjoy, and if you are teaching this stuff, I hope you'l
From playlist Recent videos
Find all the zeros using the difference of two cubes
👉 Learn how to find the zeroes of a polynomial equation/expression involving the sum/difference of two cubes. Given a polynomial having the sum of two cubes, the polynomial can be factored as follows: a^3 + b^3 = (a + b)(a^2 - ab + b^2). Similarly, given a polynomial having the difference
From playlist Zeros of a Polynomial by Factoring
This course is about calculus 3 and the following topics have been presented in this course in very details. ⭐ Table of Contents ⭐ ⌨️ (0:05) Sequences ⌨️ (38:21) Infinite series ⌨️ (1:07:31) The divergence and integral test ⌨️ (1:24:07) Comparison test ⌨️ (1:48:00)
From playlist Calculus
MinutePhysics Maths Trolling (Adding Past Infinity)
A response to the video "Adding past infinity" by MinutePhysics http://www.youtube.com/watch?v=kIq5CZlg8Rg Unlike convergent series, divergent series do not have limits (the sum of the first n terms, are not getting closer to a particular value as n increases). However, if we assume a d
From playlist My Maths Videos