If you find the area difference between a function and its Taylor or McLauren expansion ( the bounds of the integral being where the expanson is valid ) for each ongoing term, does some type of series form between the area differences from each ongoing term of the expansion?
One would expect that the area difference between the function and its approximate would decrease with each ongoing term of the expansion, but is there a common factor so that the errors form a geometric progression? or does it depend on said function?