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

#2. \( \sum\limits_{k=2}^{\infty}\frac{6}{k+2}+\frac{-6}{k+3}\)

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

#4. \( \sum\limits_{k=2}^{\infty}\frac{-6}{k}+\frac{6}{k+1}\)

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

#6. \( \sum\limits_{k=0}^{\infty} (-4)^{{k-1}} \)

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

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

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

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