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

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

#3. \( \sum\limits_{k=2}^{\infty} \frac{2}{k^{\frac{2}{9}}} \)

#4. \( \sum\limits_{k=-2}^{\infty}\frac{2}{k+6}+\frac{-2}{k+7}\)

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

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

#7. \( \sum\limits_{k=3}^{\infty} \frac{2}{k^{\frac{10}{3}}} \)

#8. \( \sum\limits_{k=-1}^{\infty} \frac{8^{{k}}}{[sin(2)]^{{k-1}}} \)

#9. \( \sum\limits_{k=1}^{\infty} \frac{4^k}{cos(k)} \)

#10. \( \sum\limits_{k=3}^{\infty} \frac{1}{k^{4}} \)