MATH 132 Study Guide - Midterm Guide: Repeating Decimal, Ratio Test, Ibm System P

• School: UMASS-Amherst
• Department: Mathematics
• Course: MATH 132
• Professor: All

Document Summary

Note: another, correct, way to write the answer is. 1000(cid:19)n are very wrong! (b) [8%] this is a geometric series having initial term a = 2. (a) [8%] by de nition, the sum of the series is the limit of its sequence of partial sums: Xn=1 an = lim n sn = lim n . 3n+1(cid:19) = lim n (cid:18) 1. 3 (b) [8%] for each n = 2, 3, . Notes: sn is the nth partial sum and not the nth term an so the series is not p . For (a) it"s pointless to nd a formula for an; even if you do (using an = sn sn 1), the fact that then you nd limn an = 0 does not tell you that p . 3n 1 9 an = sn sn 1 = 3n 9 3n + 27 n=1 an = 0 converges! n=1.