The Reciprocal Prime Series (this proof should be taught in calculus!)

►Get my favorite calculator app for your phone or tablet: MAPLE CALCULATOR: https://www.maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857 ►Check out MAPLE LEARN for your browser to do compute and graph math: https://www.maplesoft.com/products/learn/?p=TC-9857 ►Check out MapleSoft's YouTube channel: https://www.youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ. Thank you to MapleSoft for sponsoring today's video. What is the sum of 1/p, where p is prime? There are infinitely many prime numbers, but as they become larger they contribute smaller and smaller amounts to the sum. So, does that sum converge or diverge? In this video I want to share a really cool proof that they diverge that will play on the harmonic series and the geometric series - to famous series from calculus - as well as prime factorization to prove that indeed this must diverge. 0:00 The Reciprocal Prime Series 0:30 The Harmonic and Geometries Series 2:37 The proof of divergence 10:27 Thanks to Maple Calculator Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://beautifulequations.net/pages/trefor COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw ►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS I LOVE (affilliate link): ► https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography