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Prove that series $\sum_{n\in M(P)} \frac{1}{n}$ converges and find its sum [closed]
Let $P = \{p_1, p_2, \ldots, p_k\}$ be a finite set of prime numbers, and $M(P)$ be a set of natural numbers, whose prime divisors are in $P$. How can I prove that $$\sum_{n\in M(P)} \frac{1}{n}$$ ...