Set f be infinitely differentiable on an interval I containi

Set f be infinitely differentiable on an interval I containing 0. If there are constants c > 0, R > 0 s.t for any x in a neighborhood of 0 and every n |f^(n) (x)|

Solution

errror term of taylor series is given by

F^k+1*X^k+1/(k+1)!<C_k!/Rⁿ *(x^k+1/(k+1)!) which converges

from ratio test=|t_n+1/t_n|=c_k+1/R radius of convergence