Divergent Real Sequence to Positive Infinity/Examples
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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 $+\infty$.