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2079026015
Infinite Series Practice
Name __________
Find the partial sum of the geometric series.
#1.
\( \sum\limits_{k=2}^{11} \frac{(-10)^{{k-1}}}{8^{{k-2}}} \)
\(-3.695\)
\(-\frac{6}{7}\)
\(36.948\)
\(\frac{6}{7}\)
#2.
\( \sum\limits_{k=-2}^{3} \frac{4^{{k+2}}}{5^{{k+1}}} \)
\(-18.446\)
\(18.446\)
\(2.951\)
\(3.689\)
Determine whether the series converges or diverges.
#3.
\( \sum\limits_{k=1}^{\infty} \frac{(-9)^{{k+1}}}{(-2)^{{k+1}}} \)
\(-\frac{729}{28}\)
\(-\frac{9}{7}\)
\(\frac{81}{22}\)
diverges
#4.
\( \sum\limits_{k=-2}^{\infty} \frac{[sin(6)]^{{k}}}{5^{{k-1}}} \)
\(-0.053\)
\(-84.737\)
\(1516.328\)
\(1589.222\)
#5.
\( \sum\limits_{k=-1}^{\infty}\frac{1}{k+4}+\frac{-1}{k+5}\)
\(-0.201\)
\(-2\)
\(-\frac{1}{3}\)
\(\frac{1}{3}\)
#6.
\( \sum\limits_{k=2}^{\infty}\frac{-3}{k}+\frac{3}{k+1}\)
\(-\frac{3}{2}\)
\(0\)
\(7\)
diverges
#7.
\( \sum\limits_{k=-1}^{\infty} \frac{2^k}{sin(k)} \)
cannot be determined
converges
diverges
none of the above
#8.
\( \sum\limits_{k=1}^{\infty} \frac{5^k}{cos(k)} \)
cannot be determined
converges
diverges
none of the above
#9.
\( \sum\limits_{k=3}^{\infty} \frac{5}{k^{\frac{1}{9}}} \)
cannot be determined
converges
diverges
none of the above
#10.
\( \sum\limits_{k=1}^{\infty} \frac{-3}{k^{3}} \)
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.
\( \sum\limits_{k=-1}^{\infty} \frac{e^k}{4^k} \)
cannot be determined
converges
diverges
none of the above
#13.
\( \sum\limits_{k=0}^{\infty} \frac{3^k+1}{e^k} \)
cannot be determined
converges
diverges
none of the above
#14.
\( \sum\limits_{k=4}^{\infty} \frac{4^k}{ln(k)} \)
cannot be determined
converges
diverges
none of the above
#15.
\( \sum\limits_{k=1}^{\infty} \frac{8^{{k+1}}}{(-7)^{{k}}} \)
\(0\)
\(\frac{56}{15}\)
\(\frac{7}{15}\)
diverges
#16.
\( \sum\limits_{k=2}^{\infty}\frac{3}{k+1}+\frac{-3}{k+2}\)
\(-1\)
\(0.314\)
\(1\)
\(\frac{7}{10}\)
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