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Given the series $ \sum_n \frac 1 {p_n}, p\in \mathbb P $, show that it diverges with the help of the inequality $ p_n < n \log n+n\log\log n,\, \forall n \ge 6. $

Besides the inequality being an upper bound for the partial sums of the series I don't see how it can help me show anything, any ideas on how to tackle this problem or at least where I should begin at.

Anqa012
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1 Answers1

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Hint: $n\log(\log n) < n\log n$, and use the integral test !

Wang YeFei
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