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Infinite Series PracticeName __________

Find the partial sum of the geometric series.

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

Determine whether the series converges or diverges.

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