Thread: 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.

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.

sigma x=2 to inf

Determine if the series converges.
sigma x=2 to inf, ln(x)/x sqrt x

Wolfram says you need to use the Comparison Test, I'm trying to think of a series you could compare it to though...

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 .

Convince yourself that .
Use the basic comparison with a p-series.