Determine Whether the Series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { 3 ^ { 2 n } } { 2 ^ { 3 n + 1 } }$

question 223

Short Answer

Determine whether the series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { 3 ^ { 2 n } } { 2 ^ { 3 n + 1 } }$ is convergent or divergent. If it is convergent, find its sum.

---

Definitions:

Diffusion

The process by which molecules spread from areas of high concentration to areas of low concentration until there is an even distribution.

Healthy Bowel Elimination

The process of passing waste through and out of the bowel in a manner considered normal and healthy.

Dietary Choices

The selection of foods and beverages based on personal preferences or nutritional guidelines.

Hypertonic Solution

A solution that has a higher concentration of solutes compared to another solution, leading to osmotic pressure changes.