(1-1/2)×(1-1/3)×(1-1/4)×....×(1-1/100)
=(2/2-1/2)x(3/3-1/3)x...x(100/100-1/100)
=1/2x2/3x...x99/100
=1/100
\(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).......\left(1-\dfrac{1}{100}\right)=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.......\dfrac{99}{100}=\dfrac{1}{100}\)