Question

(1-1/4)(1-1/9)(1-1/16) .... (1-1/10000)

Answer 1

Tính:\(A=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right)...\left(1-\dfrac{1}{10000}\right)\)\(=\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{4^2}\right)...\left(1-\dfrac{1}{100^2}\right)\)\(=\dfrac{3}{2^2}.\dfrac{2.4}{3^2}.\dfrac{3.5}{4^2}...\dfrac{99.101}{100^2}\)

\(=\dfrac{2.3.4...99}{2.3.4...100}.\dfrac{3.4.5.6...101}{2.3.4...100}\)

\(=\)\(\dfrac{1}{100}.\dfrac{101}{2}=\dfrac{101}{200}\)

Answer 2

Khó thí