# Divergent Real Sequence to Positive Infinity/Examples

## Examples of Divergent Real Sequences to Positive Infinity

### Example: $n^\alpha$

Let $\alpha \in \Q_{>0}$ be a strictly positive rational number.

Let $\sequence {a_n}_{n \mathop \ge 1}$ be the real sequence defined as:

$a_n = n^\alpha$

Then $\sequence {a_n}$ is divergent to $+\infty$.

### Example: $2^n$

Let $\sequence {a_n}_{n \mathop \ge 1}$ be the real sequence defined as:

$a_n = 2^n$

Then $\sequence {a_n}$ is divergent to $+\infty$.