MATH 201 Exam 1, Spring 2008

Math 201 Quiz #1, March 10, 2008 1. (20 pts.) Evaluate each of the following limits .L . s ..l + ..l + ... +_1­ (a) lim( 4n - 3)""tI (b) lim n ~ sm(3 + n ) • (c) lim 1 2 n2-l n-'" 4n + 3 '"..-:J In n-+<x> In n 2. (20 pts.) Decide the convergence or divergence of each of the following series: 3. (20 pts.) Find Sn the nih partial sum of the series CX) ~{ J2kl_ I - J2kl+ I }, and then find the sum s of the series. 4. (20 pts .) Consider the series co '" lnn(2x-3)II, ~ n 4 /J'=I Find all values of x for which the series is convergent. distinguishing between absolute and conditional convergence. 5. (20 pts.) Letitx) = In(x2 + 5x + 4) • Find the Taylor series expansion off about the point a = I, and then. use this series, to find In) (1 ) for n = 0, 1,2,3, ... Caution: The required expansion is about a = 1.