Question

Tính bằng cách hợp lí :

\(\dfrac{1212}{1515}\)+ \(\dfrac{1212}{3535}\) + \(\dfrac{1212}{6363}\) + \(\dfrac{1212}{9999}\)

 

Answer 1

\(=\dfrac{12}{15}+\dfrac{12}{35}+\dfrac{12}{63}+\dfrac{12}{99}\)

\(=6\left(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}\right)\)

\(=6\cdot\left(\dfrac{1}{3}-\dfrac{1}{11}\right)=6\cdot\dfrac{8}{33}=\dfrac{48}{33}=\dfrac{16}{11}\)