Question

Determine the convergence or divergence of the p-series
$\displaystyle\sum\limits_(n=1)^Infinity 1/n^(ln3) showing all work. Can someone help me out? And I'm just learning latex, so bear with me.

Answer 1

\pi n=1 to infinity of 1/n^(ln3)

Answer 2

ln 3 > 1

Answer 3

So it is convergent

Answer 4

By the p-series test

Answer 5

\[\sum_{1}^{\infty}\frac{1}{n^{\ln3}}\]\[\ln3 \approx1.0986\]A p series convergeses if p > 1. As shown above, ln3 is greater than 1.

Answer 6

Great, thank you both!!