1. ## 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.

2. ## 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.

3. ## Re: prove infinite series?

sigma x=2 to inf

4. ## Re: prove infinite series?

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

5. ## 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...

6. ## Re: prove infinite series?

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

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