- #1
Lance WIlliam
- 47
- 0
Homework Statement
Finding the Radius of interval convergence of [tex]\sum[/tex] n=1(theres a infinity on the sigma), "x^n/2^n"
I really don't have a clue on which way I should go.
Just a hint would be great:)
The formula for finding the radius of convergence for a series is R = 1/L, where L is the limit of the absolute value of the ratio of consecutive terms in the series.
The radius of convergence represents the distance from the center of the series, within which the series will converge. Any values outside of this radius will cause the series to diverge.
To determine the interval of convergence, you must first find the radius of convergence. Then, you can check the endpoints of the interval by plugging them into the original series. If the series converges at the endpoints, then the interval of convergence is inclusive of those endpoints. If the series diverges at the endpoints, then the interval of convergence is exclusive of those endpoints.
The exponent in the formula for finding the radius of convergence, n, represents the degree of the terms in the series. This allows us to determine the convergence or divergence of the series based on the behavior of the terms.
If the limit of the absolute value of the ratio of consecutive terms is equal to zero, then the radius of convergence is infinite, and the series will converge for all values of x. This is known as a power series.