Is the Maclaurin series expansion of sin x related to the inclusion-exclusion principle?

Question

When I see the alternating signs in the infinite series expansion of sin x, I'm reminded of the inclusion-exclusion principle. Could there be any way to visualize it in such a way? Also, is there an elementary reason why the Taylor series approximates a function? I've read the wikipedia entry but didn't understand it so it's greatly appreciated if someone can point me in the right direction.

Answer 1

I imagine one could build a bridge connecting them. I don't like to be dogmatic about what concepts might be related. I will say this, though, I have used the inclusion-exclusion principle extensively in probability, but I never thought of it while working on the Maclaurin Series for any analytic function.

Of course, the alternating signs are a sort of adding and taking away of sorts, which could be thought of as an abstraction of the principle to the way I think of it for probability. I may find myself pondering the issue. As an initial thought, though, wouldn't then all addition and subtraction operations fall under that umbrella?

As to Taylor Series, Khan Academy's series on Taylor Series really helped me think of them in a much more intuitive way.