A=1/2 x 3/4 x 5/6 x 7/8 x.....x 79/80

Bởi vì 1/2 x 3/4 x 5./6 x...x79/80 ( tử số < mẫu số ) 

 => A < 1

Như vậy A sẽ phải lớn hơn 1/9

Cho nên ko thể chứng minh A < 1/9

2A hay A^2?

bài này có trong vũ hữu bình

làm đi bn khó quá mới hỏi chứ

\(P>\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\frac{7}{8}\cdot\cdot\cdot\frac{99}{100}\cdot\left(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot...\cdot\frac{98}{99}\right)\)

\(P>\frac{49}{50}>\frac{1}{15}\)

\(P^2<\left(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\frac{7}{8}\cdot...\cdot\frac{99}{100}\right)\cdot\left(\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot\frac{8}{9}\cdot....\cdot\frac{100}{101}\right)\)

\(P^2<\frac{1}{101}<\frac{1}{10}\)

\(\Rightarrow\frac{1}{15}

6,45

\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}\\ =\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\\ =\dfrac{1}{2}-\dfrac{1}{7}\\ =\dfrac{5}{14}\)

`Answer:`

\(A=1.\left(-2\right).3.\left(-4\right).5.\left(-6\right).7.\left(-8\right).9.\left(-10\right)\)

\(=-\left(2.3.4.5.6.7.8.9.10\right)\)

\(=-2[\left(2.3.4\right).\left(5.8.9\right).\left(6.7.10\right)]\)

\(=-\left(24.360.420\right)\)

\(=-3628800\)