Dordt College Dr. Gary De Young's Website
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Problem Set G

  1. Prove that if you add up the reciprocals of a sequence of consecutive positive integers, the numerator of the sum in lowest terms will always be odd. For example, \displaystyle \frac{1}{7}+\frac{1}{8} + \frac{1}{9} = \frac{191}{504}.
  2. Prove that if s(n) is the sum of the digits of a base-ten representation of a positive integer n then n-s(n) is always divisable by 9.
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