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Infinite Series PracticeName __________

Find the partial sum of the geometric series.

#1. \( \sum\limits_{k=-1}^{9} \frac{(-7)^{{k+1}}}{7^{{k+1}}} \)
#2. \( \sum\limits_{k=0}^{10} \frac{(-10)^{{k}}}{(-8)^{{k}}} \)

Determine whether the series converges or diverges.

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