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1564089939
Infinite Series Practice
Name __________
Find the partial sum of the geometric series.
#1.
\( \sum\limits_{k=-1}^{9} \frac{(-7)^{{k+1}}}{7^{{k+1}}} \)
\(-0.222\)
\(0.222\)
\(1.222\)
\(1\)
#2.
\( \sum\limits_{k=0}^{10} \frac{(-10)^{{k}}}{(-8)^{{k}}} \)
\(0\)
\(42.566\)
\(53.208\)
\(\frac{1}{6}\)
Determine whether the series converges or diverges.
#3.
\( \sum\limits_{k=-2}^{\infty} \frac{5^{{k}}}{(-6)^{{k+1}}} \)
\(-0.131\)
\(0.131\)
\(9\)
\(\frac{6}{11}\)
#4.
\( \sum\limits_{k=-2}^{\infty} \frac{(-4)^{{k+1}}}{5^{{k+1}}} \)
\(-\frac{25}{36}\)
\(1.119\)
\(\frac{25}{36}\)
\(\frac{5}{3}\)
#5.
\( \sum\limits_{k=2}^{\infty}\frac{-3}{k-1}+\frac{3}{k}\)
\(-1\)
\(-3\)
\(-\frac{2}{3}\)
\(4\)
#6.
\( \sum\limits_{k=1}^{\infty}\frac{2}{k}+\frac{-2}{k+1}\)
\(-1\)
\(-3\)
\(2\)
\(\frac{9}{10}\)
#7.
\( \sum\limits_{k=-1}^{\infty} \frac{5^k+2}{6k} \)
cannot be determined
converges
diverges
none of the above
#8.
\( \sum\limits_{k=-1}^{\infty} \frac{3^k}{6k^2+2} \)
cannot be determined
converges
diverges
none of the above
#9.
\( \sum\limits_{k=3}^{\infty} \frac{2}{k^{6}} \)
cannot be determined
converges
diverges
none of the above
#10.
\( \sum\limits_{k=1}^{\infty} \frac{1}{k^{\frac{9}{2}}} \)
cannot be determined
converges
diverges
none of the above
#11.
\( \sum\limits_{k=-1}^{\infty} \frac{e^k}{5^k} \)
cannot be determined
converges
diverges
none of the above
#12.
\( \sum\limits_{k=2}^{\infty} \frac{ln(k)}{3^k} \)
cannot be determined
converges
diverges
none of the above
#13.
\( \sum\limits_{k=-1}^{\infty}\tan\left(k+5\right)-\tan\left(k+6\right)\)
\(1\)
\(\frac{1}{8}\)
\(\frac{5}{8}\)
diverges
#14.
\( \sum\limits_{k=2}^{\infty}\frac{2}{k}+\frac{-2}{k+1}\)
\(-1\)
\(0.886\)
\(1\)
\(\frac{7}{9}\)
#15.
\( \sum\limits_{k=3}^{\infty} \frac{-2}{k^{7}} \)
cannot be determined
converges
diverges
none of the above
#16.
\( \sum\limits_{k=-2}^{\infty} \frac{sin(k)}{5^k} \)
cannot be determined
converges
diverges
none of the above
1
A
B
C
D
2
A
B
C
D
3
A
B
C
D
4
A
B
C
D
5
A
B
C
D
6
A
B
C
D
7
A
B
C
D
8
A
B
C
D
9
A
B
C
D
10
A
B
C
D
11
A
B
C
D
12
A
B
C
D
13
A
B
C
D
14
A
B
C
D
15
A
B
C
D
16
A
B
C
D