 # Which of the series, and which diverge? Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.) sum_{n=1}^inftyfrac{3}{sqrt n} Maiclubk 2020-10-27 Answered
Which of the series, and which diverge?
Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.)
$\sum _{n=1}^{\mathrm{\infty }}\frac{3}{\sqrt{n}}$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it Tasneem Almond
Given:
$\sum _{n=1}^{\mathrm{\infty }}\frac{3}{\sqrt{n}}$
To find the series is convergent or divergent use the ratio test for series.
$L=\underset{n\to \mathrm{\infty }}{lim}|\frac{{a}_{n+1}}{{a}_{n}}|$
If L<1, then the series is convergent.
If L>1, Then the series is divergent.
If L=1, Then the ratio test fails.
Apply ratio test
$|\frac{{a}_{n+1}}{{a}_{n}}|=\frac{\frac{3}{\sqrt{n+1}}}{\frac{3}{\sqrt{n}}}$
$=\frac{\sqrt{\frac{n}{n}}}{\sqrt{1+\frac{1}{n}}}$
$=1$
the ratio test fails
###### Not exactly what you’re looking for? Jeffrey Jordon