Question

find the macluarin series for the function xcosx.

Answer 1

\[
\cos(x) = 1 - \frac {x^2}{2!} + \frac {x^4}{4!} - \frac {x^6}{6!}+ \cdots \\
x \cos(x) =x - \frac {x^3}{2!} + \frac {x^5}{4!} - \frac {x^7}{6!}+ \cdots \\

\]
Can you write the general form?

Answer 2

could it be
\[\sum_{0}^{\infty}(-1)^{n}x ^{2n+1}/(2n)!\]