Question

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

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Answer 1

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Answer 2

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

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

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

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

Answer 3

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

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

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