In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power series.

In mathematics, a power series (in one variable) is an infinite series of the form where represents the coefficient of the n th term and c is a constant called the center of the series.

Nov 11, 2025 · In this section we will give the definition of the power series as well as the definition of the radius of convergence and interval of convergence for a power series.

But what's exciting about what we're about to do in this video is we're going to use infinite series to define a function. And the most common one that you will see in your mathematical careers is the …

Master power series with clear examples, step-by-step operations, and real-world uses. Start learning today on Vedantu!

A power series will converge provided it does not stray too far from this center. Common problems on power series involve finding the radius of convergence and the Interval of convergence of a series.

Jul 23, 2025 · Power series is a type of infinite mathematical series that involves terms with a variable raised to increasing powers to infinite level. Think of it as an infinite polynomial series , which can be …

power series, in mathematics, an infinite series that can be thought of as a polynomial with an infinite number of terms, such as 1 + x + x2 + x3 +⋯.

Illustrated definition of Power Series: An infinite series with increasing powers (exponents) of a variable. Like this: a0 + a1x...

Power series are used to approximate functions that are difficult to calculate exactly, such as tan -1 (x) and sin (x), using an infinite series of polynomials.