Question

tính tổng các phân số sau

9/20x23+9/23x26+...+9/77x80

 

Answer 1

đặt A=9/20x23+9/23x26+...+9/77x80

<=>\(A=3\left(\frac{3}{20\cdot23}+\frac{3}{23\cdot26}+...+\frac{3}{77\cdot80}\right)\)

\(\Rightarrow A=3\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80}\right)\)

\(\Rightarrow A=3\left(\frac{1}{20}-\frac{1}{80}\right)\)

\(\Rightarrow A=3\cdot\frac{3}{80}\)

\(\Rightarrow A=\frac{9}{80}\)