Answer
$\sum_{k=1}^{\infty} \dfrac{(-1)^k \ (x^{2k})}{k !}$
Work Step by Step
We are given the power series $-\dfrac{x^2}{1!}+\dfrac{x^4}{2!}-\dfrac{x^6}{3!}+\dfrac{x^8}{4!}...$
The given series can be represented in the summation form as:
$-\dfrac{x^2}{1!}+\dfrac{x^4}{2!}-\dfrac{x^6}{3!}+\dfrac{x^8}{4!}...=\sum_{k=1}^{\infty} \dfrac{(-1)^k \ (x^{2k})}{k !}$
