\(B=\left(1+\dfrac{1}{100}\right)\times\left(1+\dfrac{1}{99}\right)\times....\times\left(1+\dfrac{1}{3}\right)\times\left(1+\dfrac{1}{2}\right)\)

\(B=\dfrac{101}{100}\times\dfrac{100}{99}\times...\times\dfrac{4}{3}\times\dfrac{3}{2}\)

\(B=\dfrac{101\times100\times....\times4\times3}{100\times99\times....\times3\times2}\)

\(B=\dfrac{101}{2}\)

\(\Rightarrow B=\left(\dfrac{100}{100}+\dfrac{1}{100}\right)\times\left(\dfrac{99}{99}+\dfrac{1}{99}\right)\times...\times\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\times\left(\dfrac{2}{2}+\dfrac{1}{2}\right)\)

\(B=\dfrac{101}{100}\times\dfrac{100}{99}\times...\times\dfrac{4}{3}\times\dfrac{3}{2}\)

\(B=\dfrac{101}{2}\)( triệt tiêu các mẫu, tử giống nhau)

\(\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{5}\right)\times\left(1-\dfrac{1}{6}\right)\times\dots\times\left(1-\dfrac{1}{99}\right)\times\left(1-\dfrac{1}{100}\right)\) (sửa đề)

\(=\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\times\dots\times\dfrac{98}{99}\times\dfrac{99}{100}\)

\(=\dfrac{2\times3\times4\times5\times\dots\times98\times99}{3\times4\times5\times6\times\dots\times99\times100}\)

\(=\dfrac{2}{100}\)

\(=\dfrac{1}{50}\)

B=3/2x4/3x...........x2018/2017

=3x4x5x...........x2018/2x3x2x2x............x2017

=2x2018

=4036

A,C tương tự

=1/2*2/3*3/4*4/5*5/6=1/6

thank's nha

\(B=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2004}\right)\)

\(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2003}{2004}\)

\(B=\dfrac{1\cdot2\cdot3\cdot...\cdot2003}{2\cdot3\cdot4\cdot...\cdot2004}\)

\(B=\dfrac{1}{2004}\)

B=(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)...(1-1/2003)x(1-1/2004)

B=1/2x2/3x3/4x4/5x...x2002/2003x2003/2004

B=1/2004

(1-1/2)x(1-1/3)x(1-1/4)x....x(1-1/1996)x(1-1/997)

=1/2x2/3x3/4x....x1995/1996x1996/1997

=1x2x3x...x1995x1996/2x3x4x...x1996x1997

=1/1997

\(\Rightarrow\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{1996}{1997}\)

\(\Leftrightarrow1x\frac{1}{1997}\)\(=\frac{1}{1997}\)