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910556696
Infinite Series Practice
Name __________
Find the partial sum of the geometric series.
#1.
\( \sum\limits_{k=1}^{4} \frac{1}{(-9)^{{k+2}}} \)
\(-0.001\)
\(0.9\)
\(0\)
\(4\)
#2.
\( \sum\limits_{k=-2}^{7} \frac{(-5)^{{k}}}{8^{{k}}} \)
\(-0.976\)
\(-\frac{5}{2}\)
\(0.599\)
\(1.561\)
Determine whether the series converges or diverges.
#3.
\( \sum\limits_{k=0}^{\infty} \frac{6^{{k-1}}}{(-5)^{{k-1}}} \)
\(0.316\)
\(0\)
\(\frac{5}{11}\)
diverges
#4.
\( \sum\limits_{k=-2}^{\infty} \frac{[sin(9)]^{{k+1}}}{10^{{k}}} \)
\(-253.078\)
\(10.43\)
\(233.044\)
\(253.078\)
#5.
\( \sum\limits_{k=0}^{\infty}\tan\left(k+1\right)-\tan\left(k+2\right)\)
\(-\frac{5}{4}\)
\(0\)
\(\frac{9}{2}\)
diverges
#6.
\( \sum\limits_{k=2}^{\infty}\ln\left(k\right)-\ln\left(k+1\right)\)
\(-7\)
\(0\)
\(9\)
diverges
#7.
\( \sum\limits_{k=4}^{\infty} \frac{2^k}{ln(k)} \)
cannot be determined
converges
diverges
none of the above
#8.
\( \sum\limits_{k=4}^{\infty} \frac{4^k}{ln(k)} \)
cannot be determined
converges
diverges
none of the above
#9.
\( \sum\limits_{k=3}^{\infty} \frac{1}{k^{\frac{7}{5}}} \)
cannot be determined
converges
diverges
none of the above
#10.
\( \sum\limits_{k=3}^{\infty} \frac{-4}{k^{\frac{6}{5}}} \)
cannot be determined
converges
diverges
none of the above
#11.
\( \sum\limits_{k=1}^{\infty} \frac{e^k}{4^k} \)
cannot be determined
converges
diverges
none of the above
#12.
\( \sum\limits_{k=1}^{\infty} \frac{4^k+1}{e^k} \)
cannot be determined
converges
diverges
none of the above
#13.
\( \sum\limits_{k=1}^{\infty} \frac{e^k+2}{5^k} \)
cannot be determined
converges
diverges
none of the above
#14.
\( \sum\limits_{k=-1}^{\infty}\frac{5}{k+4}+\frac{-5}{k+5}\)
\(-\frac{3}{2}\)
\(3.131\)
\(\frac{3}{2}\)
\(\frac{5}{3}\)
#15.
\( \sum\limits_{k=2}^{\infty}\frac{-4}{k}+\frac{4}{k+1}\)
\(-2\)
\(-\frac{8}{3}\)
\(0\)
\(\frac{8}{3}\)
#16.
\( \sum\limits_{k=2}^{\infty} \frac{2^k+2}{log(k)} \)
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