Question

[minh hue]

Bài này làm như nào vậy mọi người ?

Answer 1

[HT.Phong (9A5)]

\(D=\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)...\left(1-\dfrac{1}{99^2}\right)\)

\(D=\dfrac{2^2-1}{2^2}\cdot\dfrac{3^2-1}{3^2}...\cdot\dfrac{99^2-1}{99^2}\)

\(D=\dfrac{\left(2+1\right)\left(2-1\right)}{2^2}\cdot\dfrac{\left(3+1\right)\left(3-1\right)}{3^2}\cdot...\cdot\dfrac{\left(99+1\right)\left(99-1\right)}{99^2}\)

\(D=\dfrac{3\cdot1}{2^2}\cdot\dfrac{4\cdot2}{3^2}\cdot\dfrac{5\cdot3}{4^2}\cdot\dfrac{6\cdot4}{5^2}\cdot...\cdot\dfrac{100\cdot98}{99^2}\)

\(D=\dfrac{1\cdot2\cdot3^2\cdot4^2\cdot5^2\cdot6^2\cdot...\cdot98^2\cdot99\cdot100}{2^2\cdot3^2\cdot...\cdot99^2}\)

\(D=\dfrac{2\cdot99\cdot100}{2^2\cdot99^2}\)

\(D=\dfrac{100}{2\cdot99}\)

\(D=\dfrac{50}{99}\)