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1837011231
Infinite Series Practice
Name __________
Find the partial sum of the geometric series.
#1.
\( \sum\limits_{k=-2}^{6} \frac{1}{(-1)^{{k+1}}} \)
\(-1\)
\(0\)
\(1.657\)
\(1\)
#2.
\( \sum\limits_{k=0}^{4} \frac{6^{{k-1}}}{3^{{k+2}}} \)
\(0.287\)
\(0\)
\(\frac{31}{27}\)
\(\frac{31}{54}\)
Determine whether the series converges or diverges.
#3.
\( \sum\limits_{k=0}^{\infty} \frac{9^{{k-2}}}{5^{{k+1}}} \)
\(-\frac{5}{4}\)
\(-\frac{9}{4}\)
\(0\)
diverges
#4.
\( \sum\limits_{k=1}^{\infty} 1 \)
\(0\)
\(\frac{1}{2}\)
diverges
#5.
\( \sum\limits_{k=-2}^{\infty}\ln\left(k+5\right)-\ln\left(k+6\right)\)
\(-4\)
\(-\frac{5}{3}\)
\(0\)
diverges
#6.
\( \sum\limits_{k=-1}^{\infty}\tan\left(k+3\right)-\tan\left(k+4\right)\)
\(-\frac{5}{3}\)
\(0\)
\(\frac{3}{7}\)
diverges
#7.
\( \sum\limits_{k=2}^{\infty} \frac{5^k}{cos(k)} \)
cannot be determined
converges
diverges
none of the above
#8.
\( \sum\limits_{k=-1}^{\infty} \frac{4^k+2}{e^k-2} \)
cannot be determined
converges
diverges
none of the above
#9.
\( \sum\limits_{k=3}^{\infty} \frac{-6}{k^{\frac{7}{3}}} \)
cannot be determined
converges
diverges
none of the above
#10.
\( \sum\limits_{k=1}^{\infty} \frac{1}{k^{\frac{10}{9}}} \)
cannot be determined
converges
diverges
none of the above
#11.
\( \sum\limits_{k=0}^{\infty} \frac{e^k}{4^k} \)
cannot be determined
converges
diverges
none of the above
#12.
\( \sum\limits_{k=3}^{\infty} \frac{ln(k)}{2^k} \)
cannot be determined
converges
diverges
none of the above
#13.
\( \sum\limits_{k=-2}^{\infty} \frac{4^k}{e^k} \)
cannot be determined
converges
diverges
none of the above
#14.
\( \sum\limits_{k=2}^{\infty} \frac{2^k}{ln(k)} \)
cannot be determined
converges
diverges
none of the above
#15.
\( \sum\limits_{k=-1}^{\infty} \frac{9^{{k-1}}}{[sin(-7)]^{{k+2}}} \)
\(-0.005\)
\(-0.932\)
\(0.068\)
diverges
#16.
\( \sum\limits_{k=1}^{\infty} \frac{-2}{k^{\frac{3}{2}}} \)
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