When a sequence or pattern "alternates at -1 and 1," it means that the values of the sequence switch between -1 and 1 as they progress. For example, the sequence:

$1, -1, 1, -1, 1, -1, \dots$

is alternating between 1 and -1. In mathematical terms, such alternating sequences are often represented using powers of $-1$, like:

$(-1)^n$

where $n$ is an integer that increases as you move through the sequence. For odd values of $n$, $(-1)^n$ will be -1, and for even values of $n$, it will be 1. Thus, the sequence alternates between these two values.

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Here are 5 related questions for expanding this topic:

1. How does alternating between -1 and 1 apply to infinite series?
2. Can alternating sequences be applied to geometric progressions?
3. What is the effect of alternating signs on the convergence of a series?
4. How do we represent more complex alternating patterns mathematically?
5. How can alternating signs be used in real-world applications like signal processing?

Tip: Alternating series can converge if the terms decrease in absolute value and approach 0