Before here @math.SE there was a question regarding a problem on a maths magazine. I decided to look at the link provided, and one problem proposed was (if I'm not recalling this wrongly):
Find $\sum\limits_{n = 0}^\infty {{{\left( { - 1} \right)}^n}\left[ {f\left( x \right) - {T_n}\left( x \right)} \right]} $
I'm most certain it was from the MMA.
Is this the correct wording of the problem? If so, any hints on how to solve it? I'm thinking of using the integral form of the remainder, but since I don't really know what the problem really was, I can't move on.