Sau khi thực hiện các phép tính: \(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)........\left(1-\dfrac{1}{100}\right)\) , ta có kết quả là
\(\dfrac{1}{100}\). \(\dfrac{1}{99}\). \(\dfrac{99}{100}\). \(\dfrac{1}{98}\). Hướng dẫn giải:\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)........\left(1-\dfrac{1}{100}\right)\)
\(=\left(\dfrac{2}{2}-\dfrac{1}{2}\right)\left(\dfrac{3}{3}-\dfrac{1}{3}\right)\left(\dfrac{4}{4}-\dfrac{1}{4}\right).......\left(\dfrac{100}{100}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.......\dfrac{98}{99}.\dfrac{99}{100}\)
\(=\dfrac{1}{100}\)
