A Taylor's series is a series expansion that acts as a representation of a function. A series expansion is a representation of a function as a sum of powers in one of its variables or a sum of powers of another function. A more specific form of a Taylor's series is the Maclaurin's series. The Taylor's series is an expansion about an arbitrary point, x = a, whereas a Maclaurin's series is an expansion about zero in particular, x = 0. The main advantage of using a power series representation of a function is that the value of the function at any point is equal to a convergent series and so can be approximated by its partial sums. These power series contributed greatly to the growth of calculus. They allowed mathematicians to analyze properties of functions with a single theory and to approximate values of...