MATH 126 Lecture Notes - Lecture 20: Alternating Series Test, Ratio Test, Bessel Function
Document Summary
Math 126: calculus ii - lecture 20: 8. 5 power series. A power series is a series in the form. C n xn=c 0+c1 x+c2 x2+c 3 x3+ where x is a variable and the cn"s are constants called the coefficients of the series. More generally, a series of the form or a power series centered at a. n=1 x a. C n is called a power series in (x-a) Geometric series where: convergent if x <1 divergent if x 1. For what values of x does the series (x 3)n n converge? n=1 a=3,cn= 1 n. Ratiotest : x 3 n an= x 3 n+ 1 x 3 n x 3 . Therefore, by the ratio test, the given series is convergent if x 3 >1. Test the points: x=2: n=1 (2 3)n n n=1 ( 1)n n by alternating series test, this series is convergent. (1) n this is the harmonic series, which is divergent.
