- #1
ognik
- 643
- 2
Hi - just done the integral test on the Riemann zeta series, came out to $\frac{1}{p-1}$
I can clearly see it therefore converges for P > 1, is singular for p=1, but for p < 1 I can't see why it diverges? In the limit p < 1 just gets smaller?
Would also like to check about p = 1, all I need do is say $\frac{1}{0}=\infty, \therefore$ it diverges, right?
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Continuing to explore the zeta function...
Test for convergence $ \sum_{n=1}^{\infty} \frac{1}{2n(2n+1)} $
I did this using the ratio test, how can I do it using the comparison test and zeta function?
I can clearly see it therefore converges for P > 1, is singular for p=1, but for p < 1 I can't see why it diverges? In the limit p < 1 just gets smaller?
Would also like to check about p = 1, all I need do is say $\frac{1}{0}=\infty, \therefore$ it diverges, right?
---------------------
Continuing to explore the zeta function...
Test for convergence $ \sum_{n=1}^{\infty} \frac{1}{2n(2n+1)} $
I did this using the ratio test, how can I do it using the comparison test and zeta function?
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