### Home > APCALC > Chapter 11 > Lesson 11.3.2 > Problem11-96

11-96.

Multiple Choice: Which of the series below converge?

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

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

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

1. II

1. III

1. I, III

1. I, II, III

This is an alternating harmonic series.

Think of this as $n!/e^{n}$. But $n! > e^n$.

This is the same as $3n(–1)^n$.