1. The problem statement, all variables and given/known data The function f has a Taylor series about x=2 that converges tp f(x) for all x in the interval of convergence. The nth derivative of f at x=2 is given by f^(n)(2)=((n+1)!)/3^n for n>=1, and f(2) =1. (a). write the first four terms and the general term of the Taylor series for f about x=2. (b). find the radius of convergence for the Taylor series for f about x=2. 2. Relevant equations 3. The attempt at a solution (a). F(x) = 1 + (2/3)(x-2) + (2/3)(x-2)^2 + (8/9)(x-2)^3 +...+ ((n+1)!(x-2)^n)/(3^n) This seems correct, however I am not sure, because when I atempt part b it doesnt really work. (b) Standard Ratio Test for the general term in part a = abs((n+2)(x-2))/3 <1 Does this not mean its divergent then? or am i all mixed up? Thanks for any help.