Question

Chứng minh rằng:

\(\frac{3^2}{20.23}\)+ \(\frac{3^2}{23.26}\)+ ... + \(\frac{3^2}{77.80}\)< 1

Làm đi mình tick cho :3

Answer 1

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

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

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

\(=\frac{3}{20}-\frac{3}{80}\)

\(< 1\)