MATH 201 Exam 1, Spring 2016

mvergence or divergence of each of the following give the name of the test you used.. Besar (yy (2-snt)” re E( : 5), _ 3. (12 pts.) Let S, be the n‘ partial sum of the series of positive terms SO, Gn, and suppose that lim, aneS" = 1. Find limn_.o dn and prove your answer. 4. (16 pts.) Consider the series co Wot Ssn LST 2 ys n=2 Find all values of x for which the series is convergent, distinguishing be- tween absolute and conditional convergence. 5. (24 pts.) Let f(x) = ae (a) Find the Taylor series expansion of f about the point a = 1;(b) then find f™(1) form =0,1,2,3,...;(c) also find the n‘* partial sum of the series in part (a).