Question

(1-1/3)(1-1/4)(1-1/5)......(1-1/99)(1-1/100)=???​

Answer 1

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$(1 - \frac{1}{3} )(1 - \frac{1}{4} )(1 - \frac{1}{5} )......(1 - \frac{1}{99} )(1 - \frac{1}{100} ) \\ = ( \frac{3 - 1}{3} )( \frac{4 - 1}{4} )( \frac{5 - 1}{5} )......( \frac{99 - 1}{99} )( \frac{100 - 1}{100} ) \\ = \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times ....... \times \frac{98}{99} \times \frac{99}{100} \\ = \frac{2}{100} \\ = \frac{1}{50}$

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Answer 2

Answer:

$\frac{1}{15}$