Question

Tính nhanh:

P=(1-1/3)x(1-1/3)x(1-1/4)x......x(1-1/99)x(1-1/100)

chú thích: dấu"/"là dấu phân số.

Answer 1

Xin phép sửa lại đề.

\(P=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right)\left(1-\frac{1}{100}\right)\)

\(1-\frac{1}{2}=\frac{1}{2}\)

 \(1-\frac{1}{3}=\frac{2}{3}\)

\(1-\frac{1}{4}=\frac{3}{4}\)

.........................

\(1-\frac{1}{99}=\frac{98}{99}\)

\(1-\frac{1}{100}=\frac{99}{100}\)

\(\Rightarrow P=\frac{1.2.3...98.99}{2.3.4...99.10}\)

\(P=\frac{\left(1.2.3...98.99\right)}{\left(2.3.4...99.100\right)}\)

\(P=\frac{1}{100}\)

Vậy: P = 1/100