Cahen's constant
In mathematics, Cahen's constant is defined as the value of an infinite series of unit fractions with alternating signs: C = ∑ i = 0 ∞ ( − 1 ) i s i − 1 = 1 1 − 1 2 + 1 6 − 1 42 + 1 1806 − ⋯ ≈ 0.643410546288... {\displaystyle C=\sum _{i=0}^{\infty }{\frac {(-1)^{i}}{s_{i}-1}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{6}}-{\frac {1}{42}}+{\frac {1}{1806}}-\cdots \approx 0.643410546288...} (sequence A118227 in the OEIS) Here ( s i ) i ≥ 0 {\displaystyle (s_{i})_{i\geq 0}} denotes Sylvester's sequence, which is defined recursively by s 0 = 2 ; s i + 1 = 1 + ∏ j = 0 i s j for i ≥ 0.