> Ignoring the constant term, we'll write out the ratio limit. [...]
No need to ignore the constant term: it fits the formula just fine! Evaluating ((-1)^n x^(2n)) / (2n)! at n=0 gives ((-1)^0 x^0) / 0! = (1 * 1) / 1 = 1, which is precisely the constant term.
Each of those three 1s is because the empty product, i.e. the product of an empty list of numbers, is 1. This is sensible because it means that (product of L1) * (product of L2) = product of (L1 append L2).
> Let's start with our Maclaurin series for cos(x):
> p(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - ... = 1 + \sum_{n=1}^∞ ((-1)^n x^(2n)) / (2n)!
> Ignoring the constant term, we'll write out the ratio limit. [...]
No need to ignore the constant term: it fits the formula just fine! Evaluating ((-1)^n x^(2n)) / (2n)! at n=0 gives ((-1)^0 x^0) / 0! = (1 * 1) / 1 = 1, which is precisely the constant term.
Each of those three 1s is because the empty product, i.e. the product of an empty list of numbers, is 1. This is sensible because it means that (product of L1) * (product of L2) = product of (L1 append L2).