Question

Rút gọn: B= (1-\(\frac{1}{2}\)).(1-\(\frac{1}{3}\)).(1-\(\frac{1}{4}\))...(1-\(\frac{1}{20}\))

Lm bài giải đầy đủ cho mk nha

Mk sẽ tick cho nếu bài giải đầy đủ

Answer 1

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

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

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

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

Answer 2

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

\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{18}{19}.\frac{19}{20}\)

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

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Answer 3

\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{18}{19}.\frac{19}{20}\)

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

Answer 4

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

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

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

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

Answer 5

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

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

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

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