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Infinite Series PracticeName __________

Find the partial sum of the geometric series.

#1. \( \sum\limits_{k=2}^{10} \frac{8^{{k+1}}}{(-5)^{{k-1}}} \)
#2. \( \sum\limits_{k=-1}^{8} \frac{5^{{k}}}{9^{{k+1}}} \)

Determine whether the series converges or diverges.

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