\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)
\(B=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}...\frac{19}{20}\)
\(B=\frac{1.2.3...19}{2.3.4...20}=\frac{1.\left(2.3.4...19\right)}{\left(2.3.4...19\right).20}=\frac{1}{20}\)
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{2}{3}\right).\left(1-\frac{3}{4}\right).....\left(1-\frac{19}{20}\right)\)
\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{19}{20}\)
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-\(\frac{1}{20}\))
=\(\frac{1}{2}\)*\(\frac{2}{3}\)*\(\frac{3}{4}\)*.....*\(\frac{19}{20}\)
=\(\frac{1\cdot2\cdot3\cdot4\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\)
=\(\frac{1\cdot\left(2\cdot3\cdot4\cdot...\cdot19\right)}{\left(2\cdot3\cdot4\cdot...\cdot19\right)\cdot20}\)
=\(\frac{1}{20}\)
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B = (1-1/2).(1-1-3).(1-1/4)...(1-1/2)
