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