Question

(1-1/97)*(1-1/98)*.....*(1-1/1000) =?

Answer 1

\(\left(1-\frac{1}{97}\right)\left(1-\frac{1}{98}\right)....\left(1-\frac{1}{1000}\right)\)

\(=\frac{96}{97}\times\frac{97}{98}\times....\times\frac{999}{1000}\)

\(=\frac{96\times97\times.....\times999}{97\times98\times....\times1000}\)

\(=\frac{96\times\left(97\times98\times....\times999\right)}{\left(97\times98\times.....\times999\right)\times1000}=\frac{96}{1000}=\frac{12}{125}\)

Answer 2

\(=\frac{96}{97}\times\frac{97}{98}\times...\times\frac{999}{1000}=\frac{96}{1000}=0,096\)