Question

tính: D= (1-1/2) . (1-1/3) . (1-1/4) . (1-1/5) . ...(1-1/100)

Answer 1

\(D=\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times...\times\left(1-\dfrac{1}{100}\right)\)

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

\(=\dfrac{1\times2\times3\times...\times99}{2\times3\times4\times...\times100}=\dfrac{1}{100}\)

Answer 2

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