Name:
Math 2260 Exam #3
April 13, 2012
Instructions: You are welcome to use one sheet of notes, but no other references or tools are allowed
(no textbooks, no calculators, etc.). This is a 50 minute exam; you may start working at 10:10 am
and must stop at 11:00 am. To receive full credit for a correct answer you must demonstrate how you
arrived at that answer. To receive partial credit for an incorrect answer your work must be clearly
explained.
1
∞
1. Consider the sequence (an )n=1 where
an = n2 + n
1/n
.
Does this sequence converge or diverge? If it converges, find its limit.
2
2. Does the series
∞
X
7n+1
n=1
(−1)n
6n−1
converge or diverge? If it converges, find its sum. If it diverges, explain why.
3
3. For what values of p does the series
∞
X
np
3 + n3
n=1
converge? Explain your answer.
4
4. What is the interval of convergence of the following power series? Explain your answer.
∞
X
(−1)n (x − 2)n
.
n3n
n=1
5
5. Find the Taylor series centered at x = π for the function
f (x) = sin(2x).
(It suffices to write down, say, the first three non-zero terms, but it’s even better to give the general
form.)
6