Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
with Eq. (14), we are literally two steps away from proving the Central Limit Theorem. All thanks to Jacob Bernoulli’s blast-from-the-past discovery of the product-series based formula for ‘e’. So this will be the point to fetch a few balloons, confetti, party horns or whatever. Ready? Here, we go: