Maclaurin series for sin x, cos x, and eˣ practice problems.

Problem

Find the exact value of the sum of the infinite series given below.
22π22!+2π44!...+2(1)nπ2n(2n)!+...\qquad\displaystyle2 -\frac{{{2\pi }^{2}}}{2!}+\frac{{2{\pi }^{4}}}{4!}-...+{{2\left( -1 \right)}^{n}}\frac{{{\pi }^{2n}}}{\left( 2n \right)!}+...
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4