MAT 127- Practice Exam 1-Fall 2016
NAME: Each numbered question is worth 25 points. SHOW ALL WORK! 1. Determine if each converges or diverges and justify: a) 1
X ne n2 n=1 b) 1
X 3
n2 +1 n=1 1 c) 1
X (ln n)2
n n=2 d) 1
X 1
Arc tan n n=1 e) 1
X 1
p
4 5
n n=1 2 2. Find the interval of convergence and corresponding sum: 1
X n=0 3 (4x)n
(3)n 3. Find the sum: 1
X 1
+
( n2 +4n+3 1
3n ) n=1 4 4) Determine if the following sequences converge and justify your answer: an = ln(n + 1)
ln(2n + 1) bn = ln n ln(n + 4) cn = (1)n 5 ( 1)n