For n 2 1, let p, be the n-th prime number. By the Prime Number Theorem,...

 

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For n 2 1, let p, be the n-th prime number. By the Prime Number Theorem, which was first conjectured by Carl Gauss as a teenager and later proved by Jacques Hadamard and Charles Jean de la Vallé Poussin, Pn lim n-00 n In n = 1. Use this fact to determine whether the series 1 1 1. 1 %3D Pn 3. 11 13 17 converges or diverges. 12 For n 2 1, let p, be the n-th prime number. By the Prime Number Theorem, which was first conjectured by Carl Gauss as a teenager and later proved by Jacques Hadamard and Charles Jean de la Vallé Poussin, Pn lim n-00 n In n = 1. Use this fact to determine whether the series 1 1 1. 1 %3D Pn 3. 11 13 17 converges or diverges. 12