#1. \( \sum\limits_{k=0}^{\infty} \frac{1}{(-2)^{{k+1}}} \)

#2. \( \sum\limits_{k=3}^{\infty} \frac{1}{k^{\frac{8}{5}}} \)

#3. \( \sum\limits_{k=0}^{\infty}\frac{-3}{k+3}+\frac{3}{k+4}\)

#4. \( \sum\limits_{k=2}^{\infty} \frac{4}{k^{\frac{3}{5}}} \)

#5. \( \sum\limits_{k=2}^{\infty} \frac{4^k}{ln(k)} \)

#6. \( \sum\limits_{k=1}^{\infty} \frac{-1}{k^{\frac{5}{3}}} \)

#7. \( \sum\limits_{k=0}^{\infty} \frac{2^k}{sin(k)} \)

#8. \( \sum\limits_{k=-1}^{\infty}\frac{-2}{k+3}+\frac{2}{k+4}\)

#9. \( \sum\limits_{k=2}^{\infty} \frac{ln(k)+1}{5^k} \)

#10. \( \sum\limits_{k=2}^{\infty} \frac{5^k}{log(k)} \)