Lucas Number - Relationship To Fibonacci Numbers

Relationship To Fibonacci Numbers

The Lucas numbers are related to the Fibonacci numbers by the identities

  • , and thus as approaches +∞, the ratio approaches

Their closed formula is given as:

where is the Golden ratio. Alternatively, as for the magnitude of the term is less than 1/2, is the closest integer to or, equivalently, the integer part of, also written as .

Conversely, .

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