MAT 21C Lecture Notes - Lecture 10: Absolute Convergence, Ratio Test, Antiderivative
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Because we also want to measure for absolute convergence, we do not use the. Alternating series test, which would only indicate conditionally convergence. Lim as n infinity of |a n+1 /a n | = lim as n infinity of |-3/ (n+1) = 0 < 1. The ratio test allows us to conclude that the series absolutely converges. Interval of convergence: can be +/- r(radius) around a(what the series is centered around, must check the endpoints to determine if the interval is closed or open, can converge for all x, can converge only at one point. )x 4 + n!x n only converges for x = 0. Already know we can add, subtract, multiply, and divide power series with each other. Find the derivative of this series: 1/(1-x) = 1 + x + x 2 + x 3 + + x n ; if |x| < 1 or -1 < x < 1 d/dx (1/(1-x)) = |-1/(1-x) 2 |
