Question

[Nguyên Ngọc Hòa]

chứng tỏ: 3/5.11 + 5/11.21 + 7/21.35 + 9/35.53 < 1

Answer 1

[Ác Mộng]

\(\frac{3}{5.11}+\frac{5}{11.21}+\frac{7}{21.35}+\frac{9}{35.53}=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{21}+\frac{1}{21}-\frac{1}{35}+\frac{1}{35}-\frac{1}{53}\right)=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{53}\right)=\frac{1}{10}-\frac{1}{106}<\frac{1}{10}<1\)