Question

\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{100}\right)\)

Answer 1

\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot...\cdot\left(1-\frac{1}{100}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot....\cdot\frac{99}{100}\)

\(=\frac{1\cdot2\cdot3\cdot...\cdot99}{2\cdot3\cdot4\cdot...\cdot100}\)

\(=\frac{1}{100}\)

Answer 2

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

Answer 3

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{100}\right)\)

\(\Rightarrow\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{99}{100}\)

\(\Rightarrow\frac{1.2.3.4.5......99}{2.3.4.....100}\)

Áp dụng tính chất loại bỏ dần ta được kết quả.

\(=\frac{1}{100}\)

Answer 4

\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{100}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{99}{100}\)

\(=\frac{1.2.3...99}{2.3.4...100}\)

\(=\frac{1}{100}\)