=1x2x3x...x19/2x3x...x20

=1/20

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

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

\(B=\frac{1.2.3...19}{2.3.4...20}=\frac{1.\left(2.3.4...19\right)}{\left(2.3.4...19\right).20}=\frac{1}{20}\)

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

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

Ta thấy hai phân số liên tiếp nhau, mẫu phân số thứ nhất giống với tử phân số thứ hai nên ta sẽ rút gọn chúng.

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

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

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

  =\(\frac{1\cdot2\cdot3\cdot4\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\)

   =\(\frac{1\cdot\left(2\cdot3\cdot4\cdot...\cdot19\right)}{\left(2\cdot3\cdot4\cdot...\cdot19\right)\cdot20}\)

   =\(\frac{1}{20}\)

B=( 1-1/2) (1-1/3).(1-1/4)....(1-1/20)

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

\(B=\frac{1\cdot2\cdot3\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\)

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

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

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

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

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

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

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

\(=\dfrac{1.2.3....19}{2.3.4.....20}\)

\(=\dfrac{1.2.3....19:\left(2.3.....19\right)}{2.3.4.....20:\left(2.3.4.....19\right)}\)

\(=\dfrac{1}{20}\)

=1/2.2/3.3/4.4/5.......19/20=1/20

B=1/2.2/3.3/4.4/5.....19/20

  = 1/20

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