Use the Maclaurin series of cos(x) to state the first three non zero terms of the Maclaurin Series for (1-cos x)/x^2

The series for cos(x) is

\sum_{k=0}^{\infty}(-1)^{k}\frac{x^{2k}}{(2k+1)!}

Just do as it says. Subtract from 1 and then divide that result by x^2.

This eliminates the 1 in the original series for cos(x), switches the signs, and reduces the powers of x in the numerators by a power of 2.

\sum_{k=0}^{\infty}(-1)^{k}\frac{x^{2k}}{(2k+2)!}