Question

[Phạm Minh Hiếu]

giúp mình với các bạn ơi 

Tính 

B=(1/2^2-1)x(1/3^2-1)x(1/4^2-1)...(1/1000^2-1)

cảm ơn nhìu

Answer 1

[Nguyễn Lê Phước Thịnh]

\(B=\left(\dfrac{1}{2^2}-1\right)\cdot\left(\dfrac{1}{3^2}-1\right)\cdot...\cdot\left(\dfrac{1}{1000^2}-1\right)\)

\(=\left(\dfrac{1}{2}-1\right)\cdot\left(\dfrac{1}{3}-1\right)\cdot...\cdot\left(\dfrac{1}{1000}-1\right)\cdot\left(\dfrac{1}{2}+1\right)\cdot\left(\dfrac{1}{3}+1\right)\cdot...\cdot\left(\dfrac{1}{1000}+1\right)\)

\(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-999}{1000}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot....\cdot\dfrac{1001}{1000}\)

\(=\dfrac{-1}{1000}\cdot\dfrac{1001}{2}=\dfrac{-1001}{2000}\)

Answer 2

[Phạm Minh Hiếu]

Thanks