Question

Explain why (-1)^n = 1 for any even number n.How is this possible? I thought it would equal -1. Does that mean the answer is "not possible"?

Answer 1

The expression (-1)^n means the number -1 multiplies itself n times.

So for example if n = 2, we have that:

`(-1)^2=(-1)\cdot(-1)=1`

For n = 3, we have:

`(-1)^3=(-1)\cdot(-1)\cdot(-1)=1\cdot(-1)=-1`

For n = 4:

`(-1)^4=(-1)^2\cdot(-1)^2=1\cdot1=1`

We can see that the result alternates from -1 and 1, and when n is odd, the result is -1, and when n is even, the result is 1.

So for any even number n, the result will be 1.