> Whether the infinite-series summation limits are worth knowing is questionable, though. That's more of historical interest.

A very common example is compound, continual interest accumulation. As a mathematician, I had trouble understanding how banks calculate it (as they would obviously not point me at the derivation of the formula), but it's actually a limit sum over infinitely small interest terms.

Similarly, these techniques work to explain and derive numerical methods for calculating many natural constants like e, pi etc.