- #1
grothem
- 23
- 1
Homework Statement
Evaluate the indefinite integral as a power series and find the radius of convergence
[tex]\int\frac{x-arctan(x)}{x^3}[/tex]
I have no idea where to start here. Should I just integrate it first?
A power series is a type of infinite series in mathematics that represents a function as a sum of terms, where each term is a constant multiplied by a variable raised to a power.
A power series is used to approximate a function by breaking it down into simpler polynomial functions. By adding more and more terms in the power series, the approximation becomes more accurate.
A Maclaurin series is a special type of power series where the center of the series is at x=0. It is named after Scottish mathematician Colin Maclaurin.
The coefficients in a power series can be found by using the Taylor series formula, which involves taking derivatives of the function at the center of the series. Alternatively, the coefficients can also be determined using a recurrence relation.
Power series are commonly used in calculus, physics, and engineering to approximate complicated functions and solve differential equations. They are also used in computer algorithms to calculate values of mathematical functions.