Real Sequence/Examples/(-1)^n

Examples of Real Sequence

The first few terms of the real sequence:

$S = \sequence {\paren {-1}^n}_{n \mathop \ge 1}$

are:

$-1, +1, -1, +1, \dotsc$

This is an example of the real sequence:

$S = \sequence {x^n}$

where $x = -1$.

$S$ is not monotone, either increasing or decreasing.

Sources

• 1958: J.A. Green: Sequences and Series ... (previous) ... (next): Chapter $1$: Sequences: $1$. Infinite Sequences: Example $4$
• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 4$: Convergent Sequences: $\S 4.3$: Examples: $\text{(i)}$
• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 4$: Convergent Sequences: $\S 4.16$: Example $\text{(iv)}$