The Taylor series about x = 5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x = 5 is given by f(n)(5) = (-1)ⁿn!/2ⁿ(n+ 2) and f(5) = 1/2.

(a) write the third-degree Taylor polynomial for f about z = 5, and then give a formula for the nth degree term of the full Taylor series.