MAT 21C Study Guide - Midterm Guide: Ratio Test, Absolute Convergence, Automobilclub Von Deutschland
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MAT 21C Full Course Notes
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Determine the radius and interval of convergence of the power series n(x 2)n. What is the radius and interval of convergence? (b) if you approximate sin x using the taylor polynomial of order 4 cen- tered at x = . 2 , what is a (reasonable) bound for the error when. Determine the radius and interval of convergence of the power series. Solution: first we use the root test to determine for which values of x the series converges absolutely. 3n+1 r n lim n n|x 2|n. |x 2| < 3, and diverges if radius of convergence of the power series is 3. n=1 |an| converges if. To nd the interval of convergence we have to test the endpoints, which are x = 1, 5. At x = 1, the series is n( 3)n. 3 n=1 n=1 which diverges because the terms don"t go to 0 as n goes to innity.
