Question

Chứng minh rằng A<4:

     A=15/11+5/12+11/13+9/14

Answer 1

\(A=\frac{15}{11}+\frac{5}{12}+\frac{11}{13}+\frac{9}{14}\)

\(\Rightarrow A=\left(1+\frac{4}{11}\right)+\left(1-\frac{7}{12}\right)+\left(1-\frac{2}{13}\right)+\left(1-\frac{5}{14}\right)\)

\(\Rightarrow A=\left(1+1+1+1\right)-\left(\frac{7}{12}-\frac{4}{11}+\frac{2}{13}+\frac{5}{14}\right)\)

\(\Rightarrow A=4-\left(\frac{7}{12}-\frac{4}{11}+\frac{2}{13}+\frac{5}{14}\right)< 4\)