The expression \(1 - (-1)^n\) changes depending on the value of \(n\). Here's how it works:

- When \(n\) is **even** (\(n = 0, 2, 4, \dots\)), \((-1)^n = 1\), so the expression becomes:
  \[
  1 - (-1)^n = 1 - 1 = 0
  \]

- When \(n\) is **odd** (\(n = 1, 3, 5, \dots\)), \((-1)^n = -1\), so the expression becomes:
  \[
  1 - (-1)^n = 1 - (-1) = 1 + 1 = 2
  \]

In summary:
- If \(n\) is even, the result is 0.
- If \(n\) is odd, the result is 2.

Would you like more details on this, or do you have any other questions?

Here are five related questions to consider:
1. What is the result of \( (-1)^n \) for fractional values of \(n\)?
2. How does the expression change if you modify it to \(1 + (-1)^n\)?
3. What happens if the base is a number other than \(-1\), such as \(2^n\)?
4. How does the sequence \( (-1)^n \) behave as \(n\) increases without bound?
5. How can this expression be used in piecewise functions?

**Tip:** The behavior of powers of \(-1\) is very useful for defining alternating sequences in mathematics!

Explore the behavior of the expression 1 - (-1)^n, which depends on whether n is even or odd. Learn the step-by-step solution to this problem, including key algebraic concepts and the properties of exponents. Suitable for students in Grades 9-11.

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