Mark44 said:Have you looked at the alternating series test?
A power series is a mathematical representation of a function as an infinite sum of powers of a variable. It has the form ∑n=0∞c_nx^n, where c_n is a coefficient and x is the variable.
Functions are represented as power series by expanding them around a particular point, usually 0, and expressing them in the form of a power series with coefficients determined by the derivatives of the function at that point.
The interval of convergence for a power series is the range of values for the variable x for which the series converges. It is determined by the ratio test or the root test, and can be open, closed, or half-open depending on the convergence behavior of the series.
Power series can be used to approximate functions by truncating the series to a finite number of terms. This results in a polynomial function that closely approximates the original function within the interval of convergence.
Power series have many practical applications in fields such as physics, engineering, and finance. They can be used to model physical phenomena, approximate complex functions in engineering problems, and calculate financial derivatives such as option prices.