Sigma notation (Recursive Series)

Question

The recursive series is $1 - 1 + 1/2 - 1/6 + 1/24 - 1/120$.

As of right now, I have $$\sum_{n=0}^5 \frac {(-1)^k}{k!}$$

Answer 1

Multiply $\dfrac{1}{k!}$ by $(-1)^n$ which will alternate for even and odd $n$.