MATH 1132Q Midterm: Exam 2 Spring 2015 Solutions

• School: UConn
• Department: Mathematics
• Course: MATH 1132Q
• Professor: All

Document Summary

If the nth partial sum of a series then an = Xn=1 an is sn = 1 + n. 1 sn = a1 + a2 + a3 + . an 1 + an = sn 1 + an. 3n 1 ) = n 3(n 1) n 1. If lim n an = 0 then the series. A counter example an converges. (c) t f. 1 n is a divergent p-series (p = 1) Xk=1 ( 1)k k3 converges conditionally. (d) t f. 1 k3 is a convergent p-series (p = 3 > 1) 2 the given series is absolutely convergent, not conditionally convergent. 1 n is a divergent p-series (p = 1) is a convergent series. |an| converges then an diverges then an converges. The sequence an = ln (2n) ln (n) converges to 1. (f) t f. = lim n ln (2) + ln (n) ln (n) Or, use l"hospital"s rule on ln (2x) ln (x)