\(=\frac{1}{2}\times\frac{2}{3}\times....\times\frac{2003}{2004}\)

\(=\frac{1\times2\times3\times...\times2003}{2\times3\times4\times...\times2014}\)

\(=\frac{1}{2014}\)

\(d=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right).........\left(1+\frac{1}{99.101}\right)\)

    \(=\frac{4}{3}.\frac{9}{2.4}.............\frac{10000}{99.101}\)

    \(=\frac{2.2}{3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}............\frac{100.100}{99.101}\)

    \(=\frac{2.3.4..........100}{2.3.4............99}.\frac{2.3.4...........100}{3.4...........101}\)

     \(=100.\frac{2}{101}\)\(=\frac{200}{101}\)

\(C=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{1994}\right)\)

    \(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{1993}{1994}\)

    \(=\frac{1\times2\times3\times...\times1993}{2\times3\times4\times...\times1994}\)

    \(=\frac{1}{1994}\)                         (Giản ước còn lại như này)

biết làm bài 1 thôi

\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\cdot\cdot\cdot\times\left(\frac{1}{999}+1\right)\)

= \(\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdot\cdot\cdot\times\frac{1000}{999}\)

lượt bỏ đi còn :

\(\frac{1000}{2}=500\)

nhanh lên nhé

(1+\(\frac{1}{3}\)) x (1+\(\frac{1}{2x4}\)) x(1+\(\frac{1}{3x5}\))x(1+\(\frac{1}{4x6}\)) x .....x (1+ \(\frac{1}{2009x2011}\))

= \(\frac{2}{1x3}\)x \(\frac{2}{2x4}\)x \(\frac{2}{3x5}\)x \(\frac{2}{4x6}\)x....x \(\frac{2}{2009x2011}\)

= ..................

đến đây tự làm nhé

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{2002}{2003}\cdot\frac{2003}{2004}\)

\(=\frac{1\cdot2\cdot3\cdot....\cdot2002\cdot2003}{2\cdot3\cdot4\cdot5\cdot....\cdot2003\cdot2004}\)

\(=\frac{1}{2004}\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{2003}{2004}=\frac{1\cdot2\cdot3\cdot4....2003}{2\cdot3\cdot4\cdot5....2004}=\frac{1}{2004}\)

Ta đặt A = giá trị biểu thúc trên 

A =3/2 * 4/3 * ....*99/98 *100/99

A = 100/2 =50 

Vậy giá trị của biểu thức trên =50

Cộng trpng ngoặc trước sẽ ra

\(A=\frac{1}{2}\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)...\left(1+\frac{1}{2015\cdot2017}\right)\)\(A=\frac{1}{2}\left(\frac{1\cdot3+1}{1\cdot3}\right)\left(\frac{2\cdot4+1}{2\cdot4}\right)...\left(\frac{2015\cdot2017+1}{2015\cdot2017}\right)\)

\(A=\frac{1^2}{2}\cdot\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\cdot\cdot\frac{2016^2}{2015\cdot2017}\)

\(A=\frac{1^2\cdot2^2\cdot3^2\cdot\cdot\cdot2016^2}{2\cdot1\cdot3\cdot2\cdot4\cdot\cdot\cdot2015\cdot2017}\)

\(A=\frac{2016}{2017}\)