Question

find the Maclaurin series for (x^2)cos(x). find the interval of convergence of the series.

Answer 1

\[\cos x = \sum_{n=0}^{\infty} (-1)^n {{x^{2n}} \over {(2n)!}}\]

so\[ x^2\cos x = \sum_{n=0}^{\infty} (-1)^n {{x^{2n+2}} \over {(2n)!}}\]

Answer 2

interval of convergence \[(-\infty,\infty)\]