Engineering Math II – Spring 2015
Name:
Quiz #7
Section: 561 / 562 / 563
Directions. Read each problem carefully and work it out on a separate sheet of paper.
Put a box around the choice you believe best answers the question. Turn in your work
with this sheet of paper stapled on top.
Problem 1 (4 pts). Which of the following four alternating series are convergent?
(i)
∞
X
(−1)
n+1
n=1
(ii)
∞
X
(−1)n−1
n=1
(iii)
∞
X
(iv)
n=1
ln(n)
n
(−1)n sin
n=1
∞
X
n2
n3 + 4
(−1)n
π n
3n − 1
.
2n − 1
(a) None of the series converge.
(b) All of the series converge.
(c) Only i and ii converge.
(d) Only iii and iv converge.
(e) Only i, ii and iii converge.
MATH 152:561-563 – Spring 2015
Quiz #6
2
Problem 2 (4 pts). What is the smallest value of n for which the nth partial sum of
P∞ (−1)n−1 n2
estimates the sum of the series correctly to four decimal places?
n=1
10n
(a) n = 4
(b) n = 5
(c) n = 6
(d) n = 7
(e) n = 8
Problem 3 (4 pts). The series
∞
X
n
is
(−1)n √
2
n +2
n=1
(a) convergent but not absolutely convergent.
(b) absolutely convergent but not convergent.
(c) both convergent and absolutely convergent.
(d) divergent.
(e) None of the above.
Problem 4 (4 pts). The series
∞
X
(−10)n
n=1
n!
is
(a) convergent but not absolutely convergent.
(b) absolutely convergent but not convergent.
(c) both convergent and absolutely convergent.
(d) divergent.
(e) None of the above.
MATH 152:561-563 – Spring 2015
Quiz #6
3
Problem 5 (4 pts). For which of the following four series is the ratio test inconclusive?
∞
X
1
(i)
n3
n=1
∞
X
n
(ii)
2n
n=1
(iii)
∞
X
(−3)n−1
√
n
n=1
√
∞
X
n
(iv)
.
1 + n2
n=1
(a) All of them.
(b) None of them.
(c) (a) and (b) only.
(d) (a) and (d) only.
(e) (b) and (c) only.