# prove infinite series?

• Nov 18th 2012, 06:08 AM
jnbbieber
prove infinite series?
How do I prove this series converges?
ln x/x^(3/2)
I think it converges to 0 by using L'Hopital and limits but am not confident in my solving.
• Nov 18th 2012, 06:28 AM
HallsofIvy
Re: prove infinite series?
Series? Are you summing over x? Is x restricted to the positive integers? Since each term is positive, it certainly cannot sum to 0!

Or do you mean simply a limit? As x goes to what value? Please post the entire statement of the problem.
• Nov 18th 2012, 06:30 AM
jnbbieber
Re: prove infinite series?
sigma x=2 to inf
• Nov 18th 2012, 06:41 AM
jnbbieber
Re: prove infinite series?
Determine if the series converges.
sigma x=2 to inf, ln(x)/x sqrt x
• Nov 18th 2012, 08:12 AM
Prove It
Re: prove infinite series?
Wolfram says you need to use the Comparison Test, I'm trying to think of a series you could compare it to though...
• Nov 18th 2012, 08:25 AM
Plato
Re: prove infinite series?
Quote:

Originally Posted by jnbbieber
How do I prove this series converges?
ln x/x^(3/2) I think it converges to 0 by using L'Hopital and limits but am not confident in my solving.

Assuming this problem is $\sum\limits_{k = 2}^\infty {\frac{{\ln (k)}}{{\sqrt[2]{{k^3 }}}}}$.

Convince yourself that $\ln(k)\le 3\sqrt[3]{k}$.
Use the basic comparison with a p-series.