Question

tính nhanh:

(\(\frac{1}{2}\)- 1 )X(\(\frac{1}{3}\)- 1)X(\(\frac{1}{4}\)- 1)X.........X(\(\frac{1}{2003}\)-1)

các bạn giúp mình nha!!!!!

Answer 1

Ta có:

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

\(=\left(-\frac{1}{2}\right).\left(-\frac{2}{3}\right).\left(-\frac{3}{4}\right).....\left(-\frac{2002}{2003}\right)\)

\(=\frac{-1.-2.-3......-2002}{2.3.4.....2003}=\frac{1}{2003}\)

Answer 2

\(\left(\frac{1}{2}-1\right)\cdot\left(\frac{1}{3}-1\right)\cdot\left(\frac{1}{4}-1\right)\cdot......\cdot\left(\frac{1}{2003}-1\right)\)

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