Question

(1-\(\dfrac{1}{2}\)).(1-\(\dfrac{1}{3}\)).(1-\(\dfrac{1}{4}\))...(1-\(\dfrac{1}{199}\))

Answer 1

(1-\(\dfrac{1}{2}\)).(1-\(\dfrac{1}{3}\)).(1-\(\dfrac{1}{4}\))...(1-\(\dfrac{1}{199}\))

=\(\dfrac{1}{2}\).\(\dfrac{2}{3}\).\(\dfrac{3}{4}\)...\(\dfrac{198}{199}\)

=\(\dfrac{1.2.3...198}{2.3.4...199}\)

=\(\dfrac{1}{199}\)

Answer 2

\(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{199}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{198}{199}=\dfrac{1}{199}\)

Answer 3

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{199}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}...\dfrac{198}{199}\)

\(=\dfrac{1\cdot2\cdot3...198}{2\cdot3\cdot4...199}\)

\(=\dfrac{1}{199}\)

Answer 4

\(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{100}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{99}{100}=\dfrac{1}{100}\)

Answer 5

=1/2 .(2/3).(3/4).(4/5).......( 198/199)

=1/199

Answer 6

= 0.0.0....0

=0