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638473911
Infinite Series Practice
Name __________
Find the partial sum of the geometric series.
#1.
\( \sum\limits_{k=2}^{10} \frac{8^{{k+1}}}{(-5)^{{k-1}}} \)
\(-2745.875\)
\(-4\)
\(26.815\)
\(2745.875\)
#2.
\( \sum\limits_{k=-1}^{8} \frac{5^{{k}}}{9^{{k+1}}} \)
\(-0.032\)
\(0.128\)
\(0.449\)
\(0.808\)
Determine whether the series converges or diverges.
#3.
\( \sum\limits_{k=-2}^{\infty} \frac{(-3)^{{k-1}}}{(-8)^{{k+2}}} \)
\(-0.011\)
\(-0.059\)
\(-\frac{5}{7}\)
\(\frac{8}{5}\)
#4.
\( \sum\limits_{k=1}^{\infty} \frac{(-4)^{{k-1}}}{3^{{k-2}}} \)
\(-9\)
\(-\frac{27}{28}\)
\(-\frac{4}{7}\)
diverges
#5.
\( \sum\limits_{k=-2}^{\infty}\frac{-2}{k+3}+\frac{2}{k+4}\)
\(-2\)
\(0\)
\(2\)
diverges
#6.
\( \sum\limits_{k=1}^{\infty}\frac{-6}{k+2}+\frac{6}{k+3}\)
\(-1\)
\(-2\)
\(-\frac{1}{2}\)
\(0\)
#7.
\( \sum\limits_{k=3}^{\infty} \frac{3^k}{ln(k)} \)
cannot be determined
converges
diverges
none of the above
#8.
\( \sum\limits_{k=0}^{\infty} \frac{5^k+1}{2k} \)
cannot be determined
converges
diverges
none of the above
#9.
\( \sum\limits_{k=1}^{\infty} \frac{-5}{k^{\frac{2}{5}}} \)
cannot be determined
converges
diverges
none of the above
#10.
\( \sum\limits_{k=1}^{\infty} \frac{-2}{k^{\frac{5}{2}}} \)
cannot be determined
converges
diverges
none of the above
#11.
\( \sum\limits_{k=0}^{\infty} \frac{2^k+1}{cos(k)} \)
cannot be determined
converges
diverges
none of the above
#12.
\( \sum\limits_{k=1}^{\infty} \frac{e^k}{2^k} \)
cannot be determined
converges
diverges
none of the above
#13.
\( \sum\limits_{k=2}^{\infty} \frac{4^k}{5k^2} \)
cannot be determined
converges
diverges
none of the above
#14.
\( \sum\limits_{k=1}^{\infty} \frac{2^k}{sin(k)} \)
cannot be determined
converges
diverges
none of the above
#15.
\( \sum\limits_{k=0}^{\infty}\ln\left(k+2\right)-\ln\left(k+3\right)\)
\(-1\)
\(-\frac{7}{5}\)
\(0\)
diverges
#16.
\( \sum\limits_{k=1}^{\infty} \frac{(-5)^{{k+1}}}{(-7)^{{k-2}}} \)
\(-766.079\)
\(-\frac{1225}{2}\)
\(153.579\)
\(\frac{1225}{2}\)
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