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

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

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

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

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

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

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

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

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

\(B=\frac{12}{11}x\frac{13}{12}x.......x\frac{16}{15}\)

\(=\frac{16}{11}\)

Bài 1a:

A = \(\frac{7^2}{7.8}\times\frac{8^2}{8.9}\times\ldots\times\frac{11^2}{11.12}\)

A = \(\frac{7.8.9.\ldots11}{7.8.\ldots11}\) x \(\frac{7.8.9\ldots11}{8.9.12}\)

A = 7/12

Bài 1a:

A = \(\frac{7^2}{7.8}\times\frac{8^2}{8.9}\times\ldots\times\frac{11^2}{11.12}\)

A = \(\frac{7.8.9.\ldots11}{7.8.\ldots11}\) x \(\frac{7.8.9\ldots11}{8.9.12}\)

A = 7/12

Bài 1B

B = (1+ 1/11).(1 + 1/12)...(1+ 1/15)

B = (11/11 + 1/11).(12/12 + 1/12)...(15/15+ 1/15)

B = 12/11.13/12....16/15

B = 16/11

a, \(A=\frac{22}{27}\)

b,\(B=\frac{1}{57}\)

C,\(C=\frac{1}{50}\)

d, \(D=0\)

Câu a:

A = -1/2 - (-3)/5 + (-1/9) + 1/27 + 7/18 + 4/35 - (-2/7)

A = -1/2 + 3/5 - 1/9 + 1/27 + 7/18 + 4/35 + 2/7

A = (-1/2 - 1/9 + 7/18 + 1/27) + (3/5 + 4/35 + 2/7)

A = (-27/54 - 6/54 + 21/54 + 2/54) + (21/35 + 4/35 + 10/35)

A = -10/54 + 1

A = -5/27 + 1

A = 22/27

Câu a:

A = (1\(\frac16\) x \(\frac67\) x 6 : \(\frac35\)) : (4\(\frac15\) x \(\frac{10}{11}\) + 5\(\frac{2}{10}\))

A = (7/6 x 6/7 x 6 x 5/3) :(21/5 x 10/11 + 52/10)

A = (1 x 6 x 5/3) : (210/55 + 26/5)

A = 10 : (210/55 + 286/55)

A = 10 : (496/55)

A = 10 x 55/496

A = 275/248

Câu b:

B = \(1\)\(\frac{13}{15}\) x 25% x 3 + (8/15 - 79/60) : 1\(\frac{23}{4}\)

B = 28/15 x 1/4 x 3 + (32/60 - 79/60) : 27/4

B = 7/15 x 3 - 47/60 x 4/27

B = 7/5 - 47/405

B = 104/81

\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\cdot\cdot\left(1+\frac{1}{99}\right)\)

\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot\cdot\cdot\cdot\frac{100}{99}\)

\(=\frac{100}{2}=50\)

\(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right)\)

\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{100}{99}\)

\(=\frac{3.4.5...100}{2.3.4...99}\)

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

\(=50\)

Ta có (1-1/2).(1-1/3^2).(1-1/4^2).....(1-1/10^2)

    =(2^2-1/2^2).(3^2-1/3^2).....(10^2-1/10)

   =(1.3/2^2).(2.4/3^2).....(9.11/10^2)

  =11/20

các bạn giúp mình với nhé

\(a,\)\(-\frac{3}{5}\cdot x=\frac{1}{4}+0,75\)

\(-\frac{3}{5}\cdot x=\frac{1}{4}+\frac{3}{4}=\frac{4}{4}=1\)

\(x=1\div\left(-\frac{3}{5}\right)\)

\(x=-\frac{5}{3}\)

\(b,\)\(\left(\frac{1}{7}-\frac{1}{3}\right)\cdot x=\frac{28}{5}\times\left(\frac{1}{4}-\frac{1}{7}\right)\)

\(\left(\frac{3}{21}-\frac{7}{21}\right)\cdot x=\frac{28}{5}\cdot\left(\frac{7}{28}-\frac{4}{28}\right)\)

\(-\frac{4}{21}\cdot x=\frac{28}{5}\cdot\frac{3}{28}\)

\(-\frac{4}{21}\cdot x=\frac{3}{5}\)

\(x=\frac{3}{5}\div\left(-\frac{4}{21}\right)\)

\(x=-\frac{63}{20}\)

\(c,\)\(\frac{5}{7}\cdot x=\frac{9}{8}-0,125\)

\(\frac{5}{7}\cdot x=\frac{9}{8}-\frac{1}{8}\)

\(\frac{5}{7}\cdot x=1\)

\(x=1\div\frac{5}{7}\)

\(x=\frac{7}{5}\)

\(d,\)\(\left(\frac{2}{11}+\frac{1}{3}\right)\cdot x=\left(\frac{1}{7}-\frac{1}{8}\right)\cdot36\)

\(\left(\frac{6}{33}+\frac{11}{33}\right)\cdot x=\left(\frac{8}{56}-\frac{7}{56}\right)\cdot36\)

\(\frac{17}{33}\cdot x=\frac{1}{56}\cdot36\)

\(\frac{17}{33}\cdot x=\frac{9}{14}\)

\(x=\frac{9}{14}\div\frac{17}{33}\)

\(x=\frac{9}{14}\cdot\frac{33}{17}=\frac{297}{238}\)