\(\frac{1}{100}\)

Without calculating decide that the statement below is true or false!

  • If \(\dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{3}+\dots+\dfrac{1}{100}=\dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers, then \(m\) is divisible by \(505\).
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