Question

I need help with this practice Question #1Does the series converge or diverge? Question 2# You conclude this because the series is ________________

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

Determine whether the given series converge or diverge.

Given:

Step 1

Determine the common ratio.

$\begin{gathered} \frac{16}{27}\times\frac{9}{4}=\frac{4}{3} \\ \\ \frac{4}{9}\times\frac{3}{1}=\frac{4}{3} \\ \\ \frac{1}{3}\times\frac{4}{1}=\frac{4}{3} \end{gathered}$

It is enough to see that it is a geometric series.

Step 2

List out the conditions for convergence /divergence of a geometric series.

• If the absolute value of the ,common ration, i.e, |r| is less than 1,, the the series ,converges,.

,

• If, |r| > 1, then the series, diverges.

Clearly, 4/3 > 1

This implies |r| >1, hence the series diverges.

ANSWER

The series diverges.

The series is geometric and the absolute value of the common ratio is greater than 1.