I have a quick question about Taylor's Theorem.
Questions
For an infinitely differentiable function, if the error term in Taylor's Theorem tends to zero, does the existance of a Taylor series follow from the fact the series and the partial sum to N can differ by at most $R_N$ (where this is the error from Taylor's Theorem), which tends to 0, meaning we can make the difference as small as we like and hence they are the same?
I hope that is clear. If not please let me know. Feel free to also post short comments as answers.