Download
1 / 8
80 likes | 129 Views
Power series are infinite series with the form Σ c_n * (x - a)^n, where c_n is a constant coefficient, a is the center, and x is the variable. Learn about convergence criteria, radius of convergence, and interval of convergence for power series.
E N D
Power Serieshttp://calculusapplets.com/powerseries.html If x is a variable, then an infinite series of the form Is called a power series. More generally, series of the form Is called a power series center at c, where c is a constant.
Convergence of a Power Series For a power series center at c, precisely one of the following is true. • The series converges only at c. • There exists a real number R>0 such that the series converges absolutely for |x – c| < R, and diverges for |x – c| > R. • The series converges absolutely for all x. The number R is the radius of convergence of the power series. The set of all values of x for which the power series converges is the interval of convergence of the power series
Find where the power series is center and radius of convergence
