\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{100}\right).200x=4036\)

\(\Leftrightarrow\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{99}{100}.200x=4036\)

\(\Leftrightarrow\frac{1.2.3...99}{2.3.4....100}.200x=4036\)

\(\Leftrightarrow\frac{1}{100}.200x=4036\)

\(\Leftrightarrow\frac{1}{100}.200x=4036\)

\(\Leftrightarrow2x=4036\)

\(\Leftrightarrow x=4036:2=2018\)

\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{100}\right)\times200\times x=4036\)

=> \(\frac{1}{2}\times\frac{2}{3}\times...\times\frac{99}{100}\times200\times x=4036\)

=> \(\frac{1\times2\times...\times99}{2\times3\times...\times100}\times200\times x=4036\)

\(\Rightarrow\frac{1}{100}\times200\times x=4036\)

\(\Rightarrow2\times x=4036\)

=> x = 2018 

4.x+1/2.3+1/3.4+1/4.5+1/5.6=1

4.x+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6=1

4x+1-1/6=1

4x=1-5/6

4x=1/6

x=1/6:4

x=1/24

Chúc Học Tốt!!!

dễ quá đi 

\(\left(1-\frac{1}{6}\right)x\left(1-\frac{1}{7}\right)x\left(1-\frac{1}{8}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{10}\right)\)

\(=\frac{5}{6}x\frac{6}{7}x\frac{7}{8}x\frac{8}{9}x\frac{9}{10}\)

\(=\frac{1}{2}\)

=(1/1-1/6)x(1/1-1/7)x(1/1-1/8)x(1/1-19)x(1/1-1/10)

=5/6x6/6x7/8x8/9x9/10

\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=\frac{23}{16}\)

\(4x+\frac{15}{16}=\frac{23}{16}\)

\(4x=\frac{1}{2}\)

\(x=\frac{1}{8}\)

             Vậy \(x=\frac{1}{8}\)

\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=\frac{23}{16}\)

\(\Rightarrow\left(x+x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=\frac{23}{16}\)

\(\Rightarrow5x+\frac{15}{32}=\frac{23}{16}\)

\(\Rightarrow5x=\frac{23}{16}-\frac{15}{32}\)

\(\Rightarrow5x=\frac{31}{32}\)

\(\Rightarrow x=\frac{31}{32}.\frac{1}{5}=\frac{31}{160}\)

truoc tien quy dong roi tinh hoac so sanh voi 1/2 kich nhe

câu này ở trong Violympic nên mình nói luôn đáp án là 1/8

1=3/3=4/4=5/5=...

=> 1+1/1*3=3/1*3=1/1

=> 1+1/2*4=4/2*4=1/2

=>...

Bieu thuc se con lai la 1*1/2*1/3*1/4*1/5

Vay A=1/120

\(A=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{101}{100}\)

\(A=\frac{101}{2}\) (Vì các số còn lại đã bị gạch bỏ)

= 3/2 + 4/3 + 5/4  ................................ 100/99

= 100/2 = 50