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Infinite Series PracticeName __________

Find the partial sum of the geometric series.

#1. \( \sum\limits_{k=1}^{4} \frac{1}{(-9)^{{k+2}}} \)
#2. \( \sum\limits_{k=-2}^{7} \frac{(-5)^{{k}}}{8^{{k}}} \)

Determine whether the series converges or diverges.

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