Question

Tính biểu thức sau:

L=(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x ..................x(1-1/2003)x(1-1/2004)

Answer 1

Ta có: \(L=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)....\left(1-\frac{1}{2004}\right)\)

\(\Rightarrow L=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{2003}{2004}\)\(=\frac{1.2.3.4....2003}{2.3.4.....2004}=\frac{1}{2004}\)

VẬY \(L=\frac{1}{2004}\)

Answer 2

\(L=\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x.....x\left(1-\frac{1}{2003}\right)\)

\(L=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x.....x\frac{2002}{2003}\)

\(L=\frac{1x2x3x4x....x2002}{2x3x4x5x.....x2003}=\frac{1}{2003}\)