Question

\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)...\left(\frac{1}{2018}-1\right)\)

Answer 1

\(=\left(-\frac{1}{2}\right)\left(-\frac{2}{3}\right)\left(-\frac{3}{4}\right)...\left(-\frac{2017}{2018}\right)\)

Tích trên là tích của các thừa số âm và có (2018-2)+1=2017 thừa số nên có kq âm

\(=-\frac{1}{2018}\)

Answer 2

\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)...\left(\frac{1}{2018}-1\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2016}{2017}.\frac{2017}{2018}\)

\(=\frac{1}{2018}\)

Answer 3

\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)...\left(\frac{1}{2018}-1\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2016}{2017}.\frac{2017}{2018}\)

\(=\frac{1.2.3.4....2016.2017}{2.3.4.5....2017.2018}=\frac{1}{2018}\)