Question

does the series converge or diverge?

Answer 1

\sum _{n=1}^{\infty \:}\frac{8}{\sqrt{n}}

Answer 2

This is a good candidate for the integral test, since \(a_n=\dfrac{8}{\sqrt n}\) is a decreasing sequence, and you can easily compute
\[\int_1^\infty \frac{8}{\sqrt x}\,\mathrm dx\]Or you can use the fact that \(\dfrac{1}{\sqrt n}\ge\dfrac{1}{n}\) for \(n\ge1\) and compare this series to
\[\sum_{n=1}^\infty\frac{8}{n}\]Do you know anything about this series?

Answer 3

thanks i think this diverges. i attached the questions and possible responses for question 13.