- #1

Seydlitz

- 263

- 4

## Homework Statement

Test the following series for convergence or divergence.

$$\sum_{n=1}^{\infty} \frac{1}{3^{\ln n}}$$

## The Attempt at a Solution

I've tried to compare this to geometric series ##3^n## but obviously the target term is larger overall than its geometric counterpart. Comparing with the reciprocal of ##\ln n## also brings no avail because the term is smaller than the former. Ratio test gives ##ρ=1## which is inconclusive. It certainly passes preliminary test because the limit goes to 0 once n goes to infinity. I haven't done integral test because it's quite ugly and I don't know how to integrate the corresponding function.

Can you guys give me suggestion to tame this series down nicely?

Thank You