Đặt \(Q=\frac{2}{3}.\frac{4}{6}.\frac{6}{7}....\frac{400}{401}\)
Áp dụng tính chất \(\frac{a}{b}< \frac{a+m}{b+m}\left(a,b,m\inℕ^∗\right)\)ta có :
\(\frac{1}{2}< \frac{1+1}{2+1}=\frac{2}{3}\)
\(\frac{2}{3}< \frac{2+1}{3+1}=\frac{3}{4}\)
...
\(\frac{399}{400}< \frac{399+1}{400+1}=\frac{400}{401}\)
\(\Rightarrow\frac{1}{2}.\frac{3}{4}.\frac{5}{6}....\frac{399}{400}< \frac{2}{3}.\frac{4}{5}.\frac{6}{7}....\frac{400}{401}\)
Hay \(P< Q\)
\(\Rightarrow P^2< P.Q\)
\(P^2< \frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{399}{400}.\frac{2}{3}.\frac{4}{5}.\frac{6}{7}....\frac{400}{401}\)
\(P^2< \frac{1.2.3.4.....400}{2.3.4.5.....401}\)
\(P^2< \frac{1}{401}< \frac{1}{400}< \left(\frac{1}{20}\right)^2\)
Vì \(P\)và \(\frac{1}{2}\)có cùng dấu
\(\Rightarrow P< \frac{1}{2}\)
Hk tốt
p=1/2.3/4.5/6......399/400
=>p<1/2.2/4.4/6....398/400
p<1.2.4.....398/2.4.6....400
rut gon dc p<1/400<1/20
vay p < 1/20
