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Material Type: Exam; Class: Calculus II; Subject: Mathematics; University: University of Illinois - Urbana-Champaign; Term: Spring 2008;
Typology: Exams
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March 7, 2008
Problem 1: State whether the following sequences converge or diverge. Find the limit of each sequence that converges. (Show your work!)
(a)
n^2 − 2 n n^3 + 17n^2
n=
(b)
)n}∞
n=
(c)
n^2 ln n
n=
(d)
e^1 /n
n=
Problem 2: Determine whether the following series converge or diverge. For those that converge, determine the sum.
(a)
k=
k^2 − k
(b)
k=
1 − 2 k 3 k
(c)
k=
32 k−^1 4 k+
(d)
k=
(−1)k^
k k + 1
Problem 4: Determine whether or not the following series converge. Show your work—state any tests you use.
(a)
k=
2 k kk
(b)
k=
(−1)k+^
k
(c)
k=
k^2 ek
(d)
k=
k^2 + 1 2 k^2 − 3
Problem 5: For each of the series below, state whether the series converges absolutely, converges conditionally, or diverges:
(a)
k=
(−1)kk 2 k^
(b)
k=
(−1)k ln k
