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

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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


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