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PrecalculusHardWhy the Formulas Work

Why the Formulas Work · Hard problem

Evaluate 11⋅3+13⋅5+⋯+151⋅53\dfrac{1}{1\cdot 3} + \dfrac{1}{3\cdot 5} + \cdots + \dfrac{1}{51\cdot 53}.

Express your answer as a common fraction.