# What is an alternating sequence?

Oct 29, 2015

See explanation

#### Explanation:

Alternating sequence is a sequence, whose term change sign (i.e. if a term ${a}_{n}$ is positive then ${a}_{n + 1}$ is negative and vice versa)

Examples:

1. ${a}_{n} = {\left(- \frac{1}{2}\right)}^{n}$
This sequence would have terms: -1/2;1/4;-1/8;1/16;...

2. ${b}_{n} = {\left(- 1\right)}^{n}$.
This sequence would have terms: -1;1;-1;1;...

3. ${c}_{n} = {\left(- 1\right)}^{n} \cdot n$
This sequence would have terms: -1;2;-3;4;...

Note that such terms can be either convergent: ${\lim}_{n \to \infty} {a}_{n} = 0$, or divergent: ${\lim}_{n \to \infty} {b}_{n}$ does not exist