> While these equations of polynomials contain a finite number of terms, we can have polynomials with an infinite number of terms. These are called series, and one of the simplest types of series is called a geometric series.
Slightly OT, but what made infinite sums a lot more sane to me was the understanding that the sums are in fact not infinite - it's just syntactic sugar for a perfectly ordinary limit over a series of finite sums, each with one more term than the last.
E.g.,
sum(1 / 2^n) for n from 1 to +infinity
"really" means:
lim(sum(1 / 2^n) for n from 1 to m) for m -> +infinity
So no infinite loops of additions are actually involved.
Slightly OT, but what made infinite sums a lot more sane to me was the understanding that the sums are in fact not infinite - it's just syntactic sugar for a perfectly ordinary limit over a series of finite sums, each with one more term than the last.
E.g.,
"really" means: So no infinite loops of additions are actually involved.