Question

Tính nhanh:

\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right).....\left(\dfrac{1}{99}-1\right)\)

Answer 1

Ta có : \(\dfrac{-1}{2}\).\(\dfrac{-2}{3}\)\(\dfrac{-3}{4}\). ... . \(\dfrac{-98}{99}\)

=>\(\dfrac{\left(-1\right).\left(-2\right).\left(-3\right).....\left(-98\right)}{2.3.4.....99}\)

=> \(\dfrac{1}{99}\)

Tick mình nha bạn hiền.

Answer 2

(1/2-1) (1/3-1) (1/4-1) ... (1/99-1)

=(-1/2) (-2/3) (-3/4) ... (-98/99)

=(-1/99)

Vậy (1/2-1) (1/3-1) (1/4-1) ... (1/99-1)=(-1/99)

Answer 3

Đặt \(A\) \(=\) \(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{99}-1\right)\)

\(A=\left(-\dfrac{1}{2}\right)\left(-\dfrac{2}{3}\right)\left(-\dfrac{3}{4}\right)...\left(-\dfrac{98}{99}\right)\)

\(A=\dfrac{1.2.3.....98}{2.3.4.....99}\)

\(A=\dfrac{1}{99}\)