PIMSO 2022 - Mathematics - Grade 9 / Secondary 3 - National Round Question 17

Simplify $\frac{22}{70}\left(\frac74+\frac7{12}+\frac7{24}+\frac7{40}+\frac7{60}+\frac7{84}+\cdots+\frac7{180}+\frac7{220}\right)$.