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1977088462
Infinite Series Practice
Name __________
Find the partial sum of the geometric series.
#1.
\( \sum\limits_{k=-2}^{1} \frac{(-4)^{{k+1}}}{(-5)^{{k-1}}} \)
\(0\)
\(64.536\)
\(\frac{369}{4}\)
\(\frac{369}{5}\)
#2.
\( \sum\limits_{k=1}^{7} \frac{(-6)^{{k+1}}}{6^{{k-1}}} \)
\(-1\)
\(-27\)
\(-6\)
\(36\)
Determine whether the series converges or diverges.
#3.
\( \sum\limits_{k=1}^{\infty} \frac{3^{{k-1}}}{(-3)^{{k}}} \)
\(-\frac{1}{2}\)
\(\frac{1}{2}\)
\(\frac{1}{6}\)
diverges
#4.
\( \sum\limits_{k=1}^{\infty} \frac{[sin(1)]^{{k+1}}}{(-5)^{{k+1}}} \)
\(-0.024\)
\(0.024\)
\(0\)
diverges
#5.
\( \sum\limits_{k=-2}^{\infty}\frac{-4}{k+3}+\frac{4}{k+4}\)
\(-2\)
\(-4\)
\(-6\)
\(\frac{1}{3}\)
#6.
\( \sum\limits_{k=-1}^{\infty}\frac{1}{k+5}+\frac{-1}{k+6}\)
\(-\frac{7}{10}\)
\(\frac{10}{9}\)
\(\frac{1}{4}\)
\(\frac{7}{10}\)
#7.
\( \sum\limits_{k=1}^{\infty} \frac{4^k}{cos(k)} \)
cannot be determined
converges
diverges
none of the above
#8.
\( \sum\limits_{k=0}^{\infty} \frac{2^k-1}{7k^2} \)
cannot be determined
converges
diverges
none of the above
#9.
\( \sum\limits_{k=3}^{\infty} \frac{1}{k^{\frac{4}{3}}} \)
cannot be determined
converges
diverges
none of the above
#10.
\( \sum\limits_{k=3}^{\infty} \frac{-5}{k^{\frac{9}{7}}} \)
cannot be determined
converges
diverges
none of the above
#11.
\( \sum\limits_{k=-2}^{\infty} \frac{e^k}{5^k} \)
cannot be determined
converges
diverges
none of the above
#12.
\( \sum\limits_{k=0}^{\infty} \frac{5^k}{cos(k)} \)
cannot be determined
converges
diverges
none of the above
#13.
\( \sum\limits_{k=1}^{\infty} \frac{-6}{k^{\frac{5}{6}}} \)
cannot be determined
converges
diverges
none of the above
#14.
\( \sum\limits_{k=2}^{\infty} \frac{-4}{k^{\frac{10}{9}}} \)
cannot be determined
converges
diverges
none of the above
#15.
\( \sum\limits_{k=-2}^{\infty} \frac{10k^2}{5^k} \)
cannot be determined
converges
diverges
none of the above
#16.
\( \sum\limits_{k=-1}^{\infty} (-2)^{{k+2}} \)
\(-\frac{1}{6}\)
\(-\frac{2}{3}\)
\(\frac{4}{3}\)
diverges
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