Originally Posted by

**Spudwad** I am given the problem:

Show that $\displaystyle r^{ln(n)} = n^{ln(r)}$ and determine the values of r $\displaystyle (r > 0)$ for which the series $\displaystyle \sum_{n=1}^{\infty} r^{ln(n)}$ converges.

I guess my initial problem is to show that the two are equal to one another as such. However, I thought that the minimum value of r that would converge would be 0 and the max would be 1.

If someone could just walk through the initial part of:

$\displaystyle r^{ln(n)} = n^{ln(r)}$

I would be very greatful. Thanks guys.