the series of terms $\frac{1}{P_n}$, where $P_n$ is the $n^{th}$ prime number, is divergent, I know only one proof using logarithm, is there another proof?
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1Yes, there are several other proofs. Did you google this site? Look for example here, or here. Also, Wikipedia offers several proofs. – Dietrich Burde Jun 08 '17 at 19:17
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1If you look for a really elementary proof, look at Paul Erdős' proof which is given in the Wikipedia article linked by Dietrich Burde. As Steve Irwin would've said: She's a beauty. – Stefan Mesken Jun 08 '17 at 19:23
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proof using only logarithm? Could you be more precise? – clark Jun 08 '17 at 19:24
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@clark i will share this proof on the other feed as this one is closed as duplicate – Omar Jun 10 '17 at 19:12