Question

How do you use the integral test to determine the convergence or divergence of `1+1/root3(4)+1/root3(9)+1/root3(16)+1/root3(25)+...`?

Answer 1

The series:

`sum_(n=1)^oo 1/root(3)(n^2)`

is divergent.

Explanation:

We can write the series synthetically as:

`sum_(n=1)^oo 1/root(3)(n^2) = sum_(n=1)^oo 1/n^(2/3)`

This is series is divergent based on the p-series test as `2/3 < 1`