MATH 1132Q Lecture Notes - Lecture 14: Ratio Test, Bmw 1 Series
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Math 1132q , lecture 14 , section 11. 8 -- power series. The number a is the center of the series. Interval of convergence: the interval of x-values which the series will converge. Radius of convergence: the distance from the center of the series to one of the endpoints of the interval of convergence. If a power series is geometric, we can find the radius and interval of convergence using our knowledge of geometric series. In general, we will use the ratio test to determine the convergence of power series. Example: let f(x) = 1 + 7x + x^2 + 7x^3 + x^4 + 7x^5 + . Find the interval of convergence of this series, and find a explicit formula for f(x). Images created by notetaker f(x) = (1 + x^2 + x^4 + ) + (7x + 7x^3 + 7x^5 + ) 1 + 7x / 1 - x^2 gives convergence (-1 , 1) interval of convergence.
