MATH 2310H Quiz: MATH 2310 UGA 2310-Quiz11p-sol_0

• School: University of Georgia
• Department: Mathematics
• Course: MATH 2310H
• Professor: All

Document Summary

Math 2310h quiz 11 practice solutions: find the radius of convergence and interval of convergence of the power series n2(x 3)n. Solution: we apply the ratio test lim n (cid:12)(cid:12)(cid:12)(cid:12) an+1 an (cid:12)(cid:12)(cid:12)(cid:12) The above is < 1 when |x 3| < 4, so the radius of convergence is 4. When x 3 = 4 (or x = 1) we get a diverging series (the terms of the sequence do not converge to 0). When x 3 = 4 (or x = 4) we similarly get a divergent series (the terms of the sequence do not converge to 0). The interval of convergence is ( 1, 7): find the sum of the series ( 1)n. Xn=1 for those values of x that lie within the interval of convergence. Solution: the series is x (a geometric series): ( 1)n. 4 + x2 : find a power series representation for the function f (x) =