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Πώς να υπολογίσετε το Continued Fraction

Τι είναι το Continued Fraction;

Continued fractions express numbers as nested fractions: x = a₀ + 1/(a₁ + 1/(a₂ + ...)); useful for rational approximations.

Οδηγός βήμα προς βήμα

  1. 1Input decimal or fraction
  2. 2Generate continued fraction expansion
  3. 3Calculate convergents (increasingly accurate approximations)

Worked Examples

Εισαγωγή
Pi ≈ 3.14159
Αποτέλεσμα
CF = [3; 7, 15, 1, 292, ...], convergent 355/113 ≈ 3.14159 (extremely accurate)

Common Mistakes to Avoid

  • Terminating before accurate enough
  • Confusing with decimal fractions

Frequently Asked Questions

Why continued fractions?

Best rational approximations; pi convergents used in engineering.

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