Question

Let $x = -1$. Find the answer to:

Answer 1

`\it (-1)^(2k)=1;\ \ \ (-1)^(2k+1)=-1,\ \ \forall\ k \in\mathbb{N}\\ \\ S=-1+(1-1)+(1-1)+\ ...\ (1-1)=-1`

Answer 2

-1

Explanation:

Since -1 to a power will either be negative or postive 1, looking at whether the exponent is odd or even can determine if the answer is -1 or 0 (x + x^2 for instance equals 0 but x + x^2 + x^3 is -1)