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Calculus II Test 3 - MATH 211, Millersville University, Exams of Calculus

Millersville University of Pennsylvania (MU)Calculus

Millersville university's calculus ii (math 211) test 3, held on march 29, 2005, from 9:00am-9:50am. The test covers various concepts of calculus, including series convergence and divergence, sequences, and infinite series. Students are required to answer questions related to determining the tests for convergence or divergence of series and sequences, finding their limits or sums, and estimating the sums of infinite series.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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Millersville University Name
Department of Mathematics
MATH 211, Calculus II , Test 3
March 29, 2005, 9:00AM-9:50AM
Please answer the following questions. Your answers will be evaluated on their correctness,
completeness, and use of mathematical concepts we have covered. Please show all work and
write out your work neatly. Answers without supporting work will receive no credit. The
point values of the problems are listed in parentheses.
1. (8 points each) Determine whether the following series converge or diverge. You must
clearly describe the tests for convergence or divergence used in each case. If a series
converges, find its sum.
(a)
∞
X
k=0 1
3k−4
7k
(b)
∞
X
k=0 e−k−e−k−1
pf3
pf4
pf5

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Millersville University Name Department of Mathematics MATH 211, Calculus II , Test 3 March 29, 2005, 9:00AM-9:50AM

Please answer the following questions. Your answers will be evaluated on their correctness, completeness, and use of mathematical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses.

  1. (8 points each) Determine whether the following series converge or diverge. You must clearly describe the tests for convergence or divergence used in each case. If a series converges, find its sum.

(a)

∑^ ∞

k=

( 1 3 k^

7 k

)

(b)

∑^ ∞ ( e−k^ − e−k−^1

)

  1. (8 points) Determine whether the following sequence converges or diverges. You must justify your answer to receive full credit for the problem. If the sequence converges, find its limit. ak = (−1)k+^

ln k k^2

  1. (10 points each) Determine whether the following series are divergent, conditionally convergent, or absolutely convergent. You must clearly describe the tests for conver- gence or divergence used in each case.

(a)

∑^ ∞ (−3)k k^24 k

(d)

∑^ ∞

k=

k^2 + 3k + 2 k^2 + 2k + 1

(e)

∑^ ∞ (−1)k^

k^2 + 1 k^3

  1. (8 points each) Consider the following sequence.

ak =

5 k − 2 3 k + 1

(a) Determine whether the sequence is monotone increasing or monotone decreasing. You must justify your answer.

(b) Determine a bound for the sequence.