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akos.ma | ||
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divisbyzero.com
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| | | | | In my next real analysis lecture, we'll be discussing the Bolzano-Weierstrass theorem. (It says that any bounded sequence of real numbers contains a convergent subsequence.) I'll be showing my class this video in which Steve Sawin(AKA Slim Dorky) raps the complete proof of the theorem. https://www.youtube.com/watch?v=dfO18klwKHg You can read the lyrics here. He has some... | |
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mathmistakes.org
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| | | | | Last week we posted a somewhat similar mistake involving logarithms. Here's the student work: While you should feel free to comment on today's mistake independent of the e... | |
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blog.autarkaw.com
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| | | | | [AI summary] The blog post explains how to use numerical methods for solving ordinary differential equations (ODEs) by framing them as definite integrals, leveraging the second fundamental theorem of calculus, and discusses a correction to a typo in an example. | |
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ckrao.wordpress.com
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| | | In this post I would like to prove the following identity, motivated by this tweet. $latex \displaystyle n! \prod_{k=0}^n \frac{1}{x+k} = \frac{1}{x\binom{x+n}{n}} = \sum_{k=0}^n \frac{(-1)^k \binom{n}{k}}{x+k}$ The first of these equalities is straightforward by the definition of binomial coefficients. To prove the second, we make use of partial fractions. We write the expansion $latex \displaystyle... | ||
