Question

Kết quả của tích (1-\(\dfrac{1}{2}\))(1-\(\dfrac{1}{3}\))(1-\(\dfrac{1}{4}\))...(1-\(\dfrac{1}{99}\)) là:

A.\(\dfrac{1}{99}\) B.\(\dfrac{1}{97}\)

C.\(\dfrac{1}{98}\) D. \(\dfrac{1}{100}\)

Answer 1

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

Chọn A

Answer 2

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

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}....\dfrac{98}{99}\)

\(=\dfrac{1.2.3....98}{2.3.4....99}=\dfrac{1}{99}\)

- Đáp án A.

Answer 3

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\cdot...\cdot\left(1-\dfrac{1}{99}\right)\\ =\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{98}{99}\\ =\dfrac{1\cdot2\cdot3\cdot...\cdot98}{2\cdot3\cdot4\cdot...\cdot99}=\dfrac{1}{99}\)

Vậy đáp án (A) đúng.