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
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- 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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