(1-1/2)*(1-1/3)*(1-1/4)*(1-1/5)*........*(1-1/99)

• 1/99
  
  (1-1/2)*(1-1/3)*(1-1/4)*(1-1/5)*..................*(1-1/99)
  =(1/2)*(2/3)*(3/4)*(4/5)*...................*(98/99)
  Here we observe that denominator of every fraction gets cancelled with numerator of next fraction, which results into 1/99
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• 》》》(1-1/2)*(1-1/3)*(1-1/4)*(1-1/5)*........*(1-1/99)
  =》》》(1/2)*(2/3)*(3/4)*(4/5)*.......... *(97/98)*(98/99)
  =》》》 All terms get cancelled only 99 remains in denominator.
  =》》》 (1/99)
  Hence (1-1/2)*(1-1/3)*
  (1-1/4)*(1-1/5)*........*(1-1/99) =1/99.
  
  
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