Category Archives: Fibonacci sequence

Cassini’s Identity without Matrix Powers

Cassini’s identity for Fibonacci numbers says that .  The classic proof of this shows (by induction) that .  Since , Cassini’s identity follows. In this post I’m going to give a different proof involving determinants, but one that does not use … Continue reading

Posted in Fibonacci sequence, matrices | Leave a comment

An Explicit Solution to the Fibonacci Recurrence

The Fibonacci sequence is a famous sequence of numbers that starts 1, 1, 2, 3, 5, 8, 13, 21, and continues forever.  Each number in the sequence is the sum of the two previous numbers in the sequence.  It’s easy to … Continue reading

Posted in Fibonacci sequence, recurrence relations, sequences and series | Leave a comment