Dick said:How did you conclude that has radius of convergence 1/8?? Your bmp has an n! in the denominator. What does the ratio test tell you?
naspek said:to find the radius, r..
i use an / an+1
naspek said:then.. i got radius = 1/8
naspek said:i've revised back my calculation..
should i get infinity for my radius..
A power series is a mathematical series in the form of a sum of terms where each term is a constant multiplied by a variable raised to a non-negative integer power.
The radius of convergence of a power series is the distance from the center of the series to the nearest point where the series still converges. It is denoted by the letter R and can be determined using the ratio test.
The interval of convergence of a power series is determined by finding the values of the variable for which the series converges. This can be done by using the ratio test and checking the endpoints of the interval.
No, the radius of convergence of a power series cannot be negative. It is always a positive value or infinity.
The radius and interval of convergence tell us the range of values for which the power series is valid and converges. This information is important in determining the applicability and accuracy of a power series in a given situation.