Question

[Lê Thúy Hà]

Tính bằng cách thuận tiện nhất:

(1-1/4) x (1-1/9) x (1-1/16) x ... x (1-1/81) x (1-1/100)

Answer 1

[Nguyễn Lê Phước Thịnh]

\(\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{9}\right)\times...\times\left(1-\dfrac{1}{100}\right)\)

\(=\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times...\times\left(1-\dfrac{1}{10}\right)\times\left(1+\dfrac{1}{2}\right)\times\left(1+\dfrac{1}{3}\right)\times...\times\left(1+\dfrac{1}{10}\right)\)

\(=\dfrac{1}{2}\times\dfrac{2}{3}\times...\times\dfrac{9}{10}\times\dfrac{3}{2}\times\dfrac{4}{3}\times...\times\dfrac{11}{10}\)

\(=\dfrac{1}{10}\times\dfrac{11}{2}=\dfrac{11}{20}\)