Question

( 1 - \(\dfrac{1}{2}\) ) ✖ ( 1 - \(\dfrac{1}{3}\) ) ✖ ( 1 - \(\dfrac{1}{4}\) ) ✖ ( 1 - \(\dfrac{1}{5}\) ) ✖ ( 1 - \(\dfrac{1}{6}\) ) ✖ ( 1 - \(\dfrac{1}{7}\) ) ✖ (1 - \(\dfrac{1}{8}\))

Answer 1

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{7}{8}=\dfrac{1}{8}\)

Answer 2

`= 1/2 xx 2/3 xx...xx 7/8`

`= 1/8`

Answer 3

\(=\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times...\times\dfrac{6}{7}\times\dfrac{7}{8}\\ =\dfrac{1}{8}\)

Answer 4

\(\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{5}\right)\times\left(1-\dfrac{1}{6}\right)\times\left(1-\dfrac{1}{7}\right)\times\left(1-\dfrac{1}{8}\right)\)

`=(2/2-1/2)xx(3/3-1/3)xx(4/4-1/4)xx(5/5-1/5)xx(6/6-1/6)xx(7/7-1/7)xx(8/8-1/8)`

`=1/2xx2/3xx3/4xx4/5xx5/6xx6/7xx7/8`

\(=\dfrac{1\times2\times3\times4\times5\times6\times7}{2\times3\times4\times5\times6\times7\times8}\)

`=1/8`