does-i-1-p-i-converge-p-i-P-

Question Number 12414 by FilupS last updated on 21/Apr/17

does \underset{i = 1}{\sum^{\infty}} p_{i} converge, p_{i} \in P

Answered by prakash jain last updated on 22/Apr/17

There are infinitely many primes .

So the series \underset{i = 1}{\sum^{\infty}} p_{i} diverges .

Commented by FilupS last updated on 22/Apr/17

what about \underset{i = 1}{\sum^{\infty}} \frac{1}{p_{i}} ? ?

Commented by prakash jain last updated on 22/Apr/17

\frac{1}{p_{i}} also diverges, same series as \frac{1}{n}

Commented by FilupS last updated on 22/Apr/17

why is that ? can you show me why ?

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