Question

If (−1)ⁿ + (−1)⁸ = 0, then n is ______.

Options

• any positive integer

• any negative integer

• any odd number

• any even number

Answer 1

If (−1)ⁿ + (−1)⁸ = 0, then n is any odd number.

Explanation:

Given:

(−1)ⁿ + (−1)⁸ = 0 

Since 8 is an even number, we know: (−1)⁸ = 1

(−1)ⁿ + 1 = 0

(−1)ⁿ = −1

We know that (−1)ⁿ = −1 only when n is an odd number.