Question

b1 (1-1/97)*(1-1/98)*....*(1-1/1000)

Answer 1

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

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

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

\(=\frac{96}{1000}\)

\(=\frac{12}{125}\)

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Answer 2

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

\(=\frac{96}{97}\cdot\frac{97}{98}\cdot...\cdot\frac{99}{1000}\)

\(=\frac{96}{1000}=\frac{12}{125}\)