What Is the General Term of the Series $1-\frac{x^{5}}{5 !}+\frac{x^{10}}{10 !}-\frac{x^{15}}{15 !}+\cdots$

Multiple Choice

What is the general term of the series $1-\frac{x^{5}}{5 !}+\frac{x^{10}}{10 !}-\frac{x^{15}}{15 !}+\cdots$ ?

A) $\frac{(-1) ^{k} x^{5 k}}{(5 k) !}$ for $k \geq 0$
B) $\frac{(-1) ^{k+1} x^{5 k}}{(5 k) !}$ for $k \geq 0$
C) $\frac{(-1) ^{k} x^{5 k+5}}{(5 k+5) !}$ for $k \geq 0$
D) $\frac{(-1) ^{k+1} x^{5 k+1}}{(5 k+1) !}$ for $k \geq 0$