Question

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

Answer 1

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

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

\(=\dfrac{1.2.3...99}{2.3.4...100}\)

\(=\dfrac{1}{100}\)

Answer 2

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

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

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

\(=\dfrac{1}{100}\)

Answer 3

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

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

\(=\dfrac{1}{100}\)

Answer 4

(1-1/2)(1-1/3)(1-1/4)....(1-1/100)

=1/2*2/3*3/4*.....*99/100

=1*2*3*...*99/2*3*4*.....*100

=1/100