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Infinite Series PracticeName __________

Find the partial sum of the geometric series.

#1. \( \sum\limits_{k=-2}^{-1} \frac{10^{{k-1}}}{8^{{k-1}}} \)
#2. \( \sum\limits_{k=1}^{8} \frac{8^{{k}}}{(-6)^{{k-1}}} \)

Determine whether the series converges or diverges.

#3. \( \sum\limits_{k=1}^{\infty} \frac{[sin(9)]^{{k-1}}}{(-9)^{{k-1}}} \)
#4. \( \sum\limits_{k=0}^{\infty} \frac{(-7)^{{k-1}}}{9^{{k-1}}} \)
#5. \( \sum\limits_{k=0}^{\infty}\frac{1}{k+2}+\frac{-1}{k+3}\)
#6. \( \sum\limits_{k=-1}^{\infty}\frac{1}{k+3}+\frac{-1}{k+4}\)
#7. \( \sum\limits_{k=4}^{\infty} \frac{3^k}{ln(k)} \)
#8. \( \sum\limits_{k=0}^{\infty} \frac{e^k}{2^k} \)
#9. \( \sum\limits_{k=1}^{\infty} \frac{1}{k^{\frac{9}{2}}} \)
#10. \( \sum\limits_{k=1}^{\infty} \frac{1}{k^{\frac{5}{3}}} \)
#11. \( \sum\limits_{k=-2}^{\infty} \frac{3^k}{e^k} \)
#12. \( \sum\limits_{k=3}^{\infty} \frac{3^k+1}{log(k)} \)
#13. \( \sum\limits_{k=-2}^{\infty} \frac{[cos(1)]^{{k-1}}}{8^{{k+2}}} \)
#14. \( \sum\limits_{k=1}^{\infty} \frac{-5}{k^{\frac{5}{9}}} \)
#15. \( \sum\limits_{k=2}^{\infty} \frac{1}{(-3)^{{k-2}}} \)
#16. \( \sum\limits_{k=-1}^{\infty} \frac{2^k}{cos(k)} \)
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