### Home > CALC > Chapter 11 > Lesson 11.1.1 > Problem11-9

11-9.

Consider the infinite series below. For each, decide if it converges or diverges and justify your conclusion. State the test you used.

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 3 } { 5 ^ { n } }$

This is a geometric series.

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { n ! } { 4 ^ { n } }$

Use the Ratio Test.

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { 3 n - 7 }$

This is an alternating series.

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 2 } n ^ { - 1 }$

$=\frac{1}{2}\displaystyle\sum_{n=1}^\infty\frac{1}{n}$