Question

(1-\(\frac{1}{2}\))X(1-\(\frac{1}{3}\))x(1-\(\frac{1}{4}\))x.....x(1-\(\frac{1}{2015}\))x(1-\(\frac{1}{2016}\))

 

 

 

 

 

Answer 1

\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{2015}\right)\times\left(1-\frac{1}{2016}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{2014}{2015}\times\frac{2015}{2016}\)

\(=\frac{1}{2016}\)

Answer 2

Giải : Ta có                (1-1/2)*(1-1/3)*(1-1/4)*....*(1-1/2015)*(1-1/2016)  

                                = 1* -(1/2+1/3+1/4+....+1/2015+1/2016)

                                = 1* - (1/2+1/2016 +1/3+1/2015 +...+1/1007)

                                = 1* -(1/2033134)

                                = -1/2033134