Question

Answer 1

\(A=\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+...+\dfrac{1}{2023\cdot2014}\)

    \(=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{2023}-\dfrac{1}{2024}\)

    \(=\dfrac{1}{5}-\dfrac{1}{2024}=\dfrac{2019}{10120}\)

Answer 2

1/(5.6)+ 1/(6.7) + 1/(7.8) + ... + 1/(2023.2024)

= 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/2023 - 1/2024

= 1/5 - 1/2024

= 2019/10120