Power series engineering mathematics

1. What is a power series in mathematics?
2. What is the general formula of power series?
3. What is power series used for?

What is a power series in mathematics?

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 +⋯.

What is the general formula of power series?

Power series is a sum of terms of the general form aₙ(x-a)ⁿ. Whether the series converges or diverges, and the value it converges to, depend on the chosen x-value, which makes power series a function.

What is power series used for?

Power series are useful tools that can be used to expand other functions, solve equations, provide for assessment of intervals of convergence, used as trial functions, and are applied in all areas of engineering. Included in this discussion are Taylor's Series, which are extremely important in numerical approximations.