In terms of the remainder, what does it mean for a Taylor

Solution 7EStep 1:In this problem we need to say, in terms of the remainder, what does it mean for a Taylor series for a function f to converge to fSuppose f is infinitely differentiable on an open interval I that contains a point c. Suppose for each x in I, there exists a real number such that for all n and y between c and x.Let for each x in I, the remainder term for order Taylor series is for some point b between c and x.By assumption we have for all n and y between c and x.This last sequence converges to 0 for each x. This means that the Taylor series of f converges to f itself.