Home > CALC > Chapter 11 > Lesson 11.2.3 > Problem11-70

11-70.

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

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { ( - 1000 ) ^ { n } } { n ! }$

Use the Ratio Test.

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

$\frac{n}{\sqrt{n}}=\sqrt{n}$

$\lim\limits_{n\to\infty}\sqrt{n}=?$

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 6 } { n ^ { 5 / 2 } }$

This is a $p$-series.

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

This is a geometric series.