Hi, I really don't know how to prove that the following series converges..

Thanks so much!!

Everk

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- Sep 4th 2011, 06:14 PMeverkSeries Involving Prime Numbers
Hi, I really don't know how to prove that the following series converges..

Thanks so much!!

Everk - Sep 4th 2011, 07:04 PMILoveMaths07Re: Series Involving Prime Numbers
Use the integral test.

- Sep 5th 2011, 08:27 AMeverkRe: Series Involving Prime Numbers
- Sep 5th 2011, 12:45 PMOpalgRe: Series Involving Prime Numbers
I guess you need some heavy machinery for this. The n'th prime number satisfies , because of the prime number theorem. Also (obviously) and so

Therefore . But converges, by the integral test. Hence, by the comparison test, so does - Sep 5th 2011, 01:14 PMchisigmaRe: Series Involving Prime Numbers
In...

http://www.mathhelpforum.com/math-he...ers-84832.html

... it has been demonstrated that...

(1)

... where...

(2)

Now is...

(3)

... so that...

(4)

Kind regards