Question

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)^n(n!)/((2^n)(n+2)), and f(5)=1/2.
Write third degree Taylor polynomial for f about x=5. Then find the radius of convergence of the Taylor series for f about x=5.
Please help me solve this problem step by step. Thanks a lot!