Absolutely Convergent Series/Examples

Examples of Absolutely Convergent Series

Arbitrary Example

Let $S$ be the series defined as:

\(\ds S\)

\(=\)

\(\ds \sum_{n \mathop = 1}^\infty \paren {-1}^{n - 1} \paren {\dfrac 1 n}^n\)

\(\ds \)

\(=\)

\(\ds 1 - \paren {\dfrac 1 2}^2 + \paren {\dfrac 1 3}^3 - \paren {\dfrac 1 4}^4 + \cdots\)

Then $S$ is absolutely convergent.