Question

Question #743f2

Answer 1

One very common use is in determining non-arithmetic functions in calculators.

Explanation:

Your question is categorized as "applications of power series" so I'll give you an example from that realm.

One of the most common uses of power series is computing the results of functions that are not well-defined for use by computers. An example would be `sin(x)` or `e^x`.

When you plug one of these functions into your calculator, your calculator needs to be able to compute them using the arithmetic logic unit which is installed in it. This unit generally cannot directly perform an exponential or trigonometric function, but power series allow us to achieve accurate results with only addition and multiplication.

`sin(x) = sum_(n=0)^infty (-1)^n (x^(2n +1))/(2n + 1)`
`e^x = sum_(n=0)^infty x^n / (n!)`

When carried out to infinity, these power series are exactly equal to the functions they derive from. However, if all you need is 9 decimal places of accuracy, performing a partial sum up to a smaller number is sufficient. This is the method used by most modern calculators.