Question

what are some real world applications of infinite series?

Answer 1

-Fourier Series are one type of infinite series that get tons of use in physics and programming.
-Taylor Series are a valuable way to write some functions as a power series, which is sometimes used in calculators to compute the trig functions.
-Depends on if you call other areas of math "real world," but infinite series show up all the time in analysis, differential equations, and complex variables.
-They're intrinsically fascinating -- haven't you ever wondered what you get when you add up infinitely many numbers?