\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{100}\right).200x=4036\)
\(\Leftrightarrow\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{99}{100}.200x=4036\)
\(\Leftrightarrow\frac{1.2.3...99}{2.3.4....100}.200x=4036\)
\(\Leftrightarrow\frac{1}{100}.200x=4036\)
\(\Leftrightarrow\frac{1}{100}.200x=4036\)
\(\Leftrightarrow2x=4036\)
\(\Leftrightarrow x=4036:2=2018\)
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{100}\right)\times200\times x=4036\)
=> \(\frac{1}{2}\times\frac{2}{3}\times...\times\frac{99}{100}\times200\times x=4036\)
=> \(\frac{1\times2\times...\times99}{2\times3\times...\times100}\times200\times x=4036\)
\(\Rightarrow\frac{1}{100}\times200\times x=4036\)
\(\Rightarrow2\times x=4036\)
=> x = 2018
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{100}\right).200x=4036\)
\(\frac{1}{2}.\frac{2}{3}....\frac{99}{100}.200x=4036\)
\(\frac{1.2.....99}{2.3...100}.200x=4036\)
\(\frac{1}{100}.20x=4036\)
\(\frac{20x}{100}=4036\)
\(x=2018\)
Dấu ''.'' là dấu nhân nhé
\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{100}\right)\cdot200\cdot x=4036\)
\(\Rightarrow\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{99}{100}\cdot200\cdot x=4036\)
\(\Rightarrow\frac{1}{100}\cdot200\cdot x=4036\)
\(\Rightarrow2\cdot x=4036\)
\(\Rightarrow x=\frac{4036}{2}=2018\)
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{100}\right).200x=4036\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{99}{100}.200x=4036\)
\(=\frac{1.2.3.....99}{2.3.4.....100}.200x=4036\)
\(=\frac{1}{100}.200x=4036\)
\(\Rightarrow\frac{1}{100}.200x=4036\)
\(\Rightarrow200x=4036\div\frac{1}{100}\)
\(\Rightarrow200x=403600\)
\(\Rightarrow x=403600\div200\)
\(\Rightarrow x=2018\)
