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PrecalculusHardWhy the Formulas Work

Why the Formulas Work · Hard problem

Evaluate the product (1−12)(1−13)⋯(1−17)\left(1 - \dfrac{1}{2}\right)\left(1 - \dfrac{1}{3}\right)\cdots\left(1 - \dfrac{1}{7}\right).

Express your answer as a common fraction.