Question

Fill in the blanks.

For $r\_\_\_\_\_\_$, the sequence $\left\{r^k\right\}$diverges.

Short answer

The required answer is For$\left|r\right|\mathbf{>}\mathbf{1}\mathbf{}\mathbf{and}\mathbf{}\mathit{r}\mathbf{=}\mathbf{-}\mathbf{1}$, the sequence diverges.

Step-by-step solution

Step 1. Given Information

The given data is that geometric sequence diverges.

Step 2. Explanation

Using the concept of convergence and divergence of Geometric series.

Let ${\left\{r^k\right\}}_{k=0}^{\infty }$be a geometric sequence.

Then$\left\{r^k\right\}$diverges when$\left|r\right|>1andr=-1$