\begin{array}{c}
\color{#4facfe}{𝖙}
\color{#55a7fd}{𝖍}
\color{#5ea2fc}{𝖚}
\color{#679dfb}{𝖞}
\color{#7098fa}{𝖓}
\color{#7993f9}{𝖌}
\color{#828ef8}{𝖚}
\color{#8b89f7}{𝖞}
\color{#9484f6}{𝖊}
\color{#9d7ff5}{𝖓}
\color{#a67af4}{𝖙}
\color{#af75f3}{𝖍}
\color{#b870f2}{𝖎}
\color{#c16bf1}{0}
\color{#ca66f0}{3}
\color{#d361ef}{5}
\color{#dc5cee}{4}
\color{#e557ed}{9}
\end{array}

Đặt `B=2/3*4/5*6/7* ... * 1024/1025`

Ta có `:n/(n+1)=(n+1-1)/(n+1)=1-1/(n+1)`

`(n+1)/(n+2)=(n+2-1)/(n+2)=1-1/(n+2)`

Vì `n+2>n+1=>1-1/(n+1)<1-/(n+2)` hay `n/(n+1)<(n+1)/(n+2)(***)`

Áp dụng `(***)` ta được:

`1/2<2/3`

`3/4<4/5`

`...`

`1023/1024<1024/1025`

`=>A<B`

`=>A*A<A*B`

`=>A^2<(1/2*3/4* ... *1023/1024)*(2/3*4/5* ... *1024/1025)`

`=>A^2<1/1025`

Ta có `1/2025<1/2024=(1/32)^2`

`=>A^2<(1/32)^2`

`=>A<1/32`

Vậy `A<1/32`