Question

(1-1/5).(1-2/5).(1-3/5)...(1-9/5)

 

Answer 1

\(\left(1-\dfrac{1}{5}\right)\left(1-\dfrac{2}{5}\right)\cdot...\cdot\left(1-\dfrac{9}{5}\right)\)

\(=\left(1-\dfrac{5}{5}\right)\cdot\left(1-\dfrac{1}{5}\right)\cdot...\cdot\left(1-\dfrac{9}{5}\right)\)

\(=0\cdot\dfrac{4}{5}\cdot...\cdot\dfrac{-4}{5}=0\)

Answer 2

`(1-1/5).(1-2/5).(1-3/5)...(1-9/5)`

`= ( (5-1)/5)((5-2)/5)...((5-9)/5)`

`= 4/5 . 3/5 ... (-3/5) . (-4/5)`

`= (4.(-4))/(5.5) .  (3.(-3))/(5.5) . (2.(-2) )/(5.5) .  (1.(-1))/(5.5) .0`

`=0`

Answer 3

(1- 1/5) . (1-2/5). (1-3/5)...(1-9/5)

=(5/5-1/5) . (5/5- 2/5). (5/5-3/5)...(5/5-9/5)

= 4/5 . 3/5 .2/5....-4/5

=[4/5-(-4/5)].3/5.2/5

=0