Unit Fraction - Series of Unit Fractions

Series of Unit Fractions

Many well-known infinite series have terms that are unit fractions. These include:

  • The harmonic series, the sum of all positive unit fractions. This sum diverges, and its partial sums
closely approximate ln n + γ as n increases.
  • The Basel problem concerns the sum of the square unit fractions, which converges to π2/6
  • Apéry's constant is the sum of the cubed unit fractions.
  • The binary geometric series, which adds to 2, and the reciprocal Fibonacci constant are additional examples of a series composed of unit fractions.

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