Sai Đề

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

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

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

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

\(B=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}......\frac{21}{20}\)

\(B=\frac{21}{2}\)

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

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

\(\Rightarrow B=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{21}{20}\)

\(\Rightarrow B=\frac{21}{2}\)

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

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

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

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

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

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

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

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

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

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

\(B=\frac{1\cdot2\cdot3\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}=\frac{1}{20}\)