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A = \(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)...\left(\frac{1}{99}-1\right)\)

    = \(-\frac{1}{2}.\frac{-2}{3}.\frac{-3}{4}....\frac{-98}{99}\)

    = \(\frac{-1.\left(-2\right).\left(-3\right)....\left(-98\right)}{2.3.4....99}=\frac{1}{99}\)

[x-1/4]:2/3=-5/8

​x-1/4=-5/8.2/3

​ x-1/4=-5/12

x=-5/12+1/4

​x=-1/6

Chúc bn hok tốt

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[x - 1/4] : 2/3  = -5/8

 x - 1/4           = -5/8 . 2/3

 x - 1/4           = -5/12

 x                   = -5/12 + 1/4

 x                   = -1/6

a . 7/12 . 6/11 + 7/12 . 5/11 - 2 7/12

= 7/12 . ( 6/11 + 5/11 ) - 31/12

= 7/12 . 1 - 31/12

= 7/12 - 31/12

= -2

b . -5/9 . -6/13 + 5/-9 . -5/13 - 5/9

= -5/9 . ( -6/13 + -5/13 ) - 5/9

= -5/9 . ( -1 ) -5/9

= 5/9 - 5/9

= 0

Đặt A = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{100}}\)

     2A = \(2.\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{100}}\right)\)

      2A = \(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}\)

 2A - A = \(\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{100}}\right)\)

         A = \(1+\frac{1}{2^{100}}=\frac{2^{100}+1}{2^{100}}\)

\(-\frac{7}{11}.\frac{11}{19}+\frac{-7}{11}.\frac{8}{19}+\frac{-4}{11}=-\frac{7}{11}.\left(\frac{11}{19}+\frac{8}{19}\right)-\frac{4}{11}\)

\(=-\frac{7}{11}.1-\frac{4}{11}=-\frac{7}{11}-\frac{4}{11}\)

\(=-\frac{11}{11}=-1\)

\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)

\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}\)

\(B=\frac{1.2.3...19}{2.3.4...20}\)

\(B=\frac{1}{20}\)

B=(1-1/2)(1-1/3)........(1-1/20)

B=1/2.2/3.......19/20

B=1/20