According to Taylor Theorem: f(x)= Pn(x) + Rn(x), where Pn(x) is the n-th Taylor polynomial and Rn(x) is the error term.
If I have a function, I know how to derive its Taylor series. But what can I do to get the original function if I have only the Taylor series expansion, and I am given that this series converges to its function? (i.e. Rn(x) goes to zero)