7: There is a factorial of even numbers in the denominator, which clearly points to the cosine expansion. However, there is an extra k in the numerator. Typically we would get rid of it using integration of series, but here it would be quite complicated, since we would have to somehow change x2k into xx−1 before integrating. Fortunately, there is an easier alternative, namely cancelling. However, we would much prefer having 2k in the numerator. Creating it is the first step.