MAT136H1 Lecture Notes - Absolute Convergence, Alternating Series Test, Integral Test For Convergence

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #1 (easy): determining the radius and interval of convergence. Power series contain variable in the series expression so that where "s are coefficients and is a variable. Power series looks like polynomial, except with infinite terms. Sometimes restrictions apply to the possible values that can take to make the power series convergent. Ratio test can be used to determine this radius for the series convergence. Then various series tests learned so far can apply to be more specific about the interval of convergence. Find the radius of convergence and interval of convergence of the series. Notice that the series contains a variable x. Thus, the range of values that x can take which makes the series convergent need to be determined. In order to do so, first put into the ratio test and get the outcome of the ratio test which will contain the variable x.