Question

P=1/2.3/4.5/6.....399/400.Chung to rang P nho hon1/20

Answer 1

Đặt Q =\(\frac{2}{3}.\frac{4}{5}.\frac{6}{7}.\frac{8}{9}.....\frac{400}{401}\)

Dễ thấy: P < Q

Mặt khác:

P.Q = \(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}....\frac{399}{400}.\frac{400}{401}=\frac{1.2.3....399.400}{2.3.4...400.401}\)

=\(\frac{1}{401}< \frac{1}{400}=\left(\frac{1}{20}\right)^2\)

Mà \(P^2< P.Q< \left(\frac{1}{20}\right)^2\Leftrightarrow P< \frac{1}{20}\)

Answer 2