đặt \(A=\frac{3^4}{20\cdot23}+\frac{3^4}{23\cdot26}+...+\frac{3^4}{77\cdot80}\)
\(A=3^3\left(\frac{3}{20\cdot23}+\frac{3}{23\cdot26}+...+\frac{3}{77\cdot80}\right)\)
\(A=3^3\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80}\right)\)
\(A=3^3\left(\frac{1}{20}-\frac{1}{80}\right)\)
\(A=3^3\cdot\frac{3}{80}\)
\(A=\frac{3^4}{80}=\frac{81}{80}>1\)
\(\frac{3^4}{20.23}+\frac{3^4}{23.26}+...+\frac{3^4}{77.80}\)
\(=3^3\left(\frac{3}{20.23}+\frac{3}{23.26}+...+\frac{3}{77.80}\right)\)
\(=3^3\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80}\right)\)
\(=3^3\left(\frac{1}{20}-\frac{1}{80}\right)\)
\(=\frac{3^3.3}{80}\)
\(=\frac{3^4}{80}\)
\(=\frac{81}{80}\)
\(=\frac{80}{80}+\frac{1}{80}\)
\(=1+\frac{1}{80}\)
=> Biểu thức trên lớn hơn 1
