perplexus.info :: Just Math : Fibonacci Inequality

Fibonacci Inequality (Posted on 2021-05-06)

Let F_n be the nth Fibonacci number.

Prove that F²_n+1 > F_2n for all n > 1.

No Solution Yet Submitted by tomarken

Rating: 4.0000 (1 votes)

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looking online: d'Ocagne's Identity

| Comment 2 of 4 |

The inequality follows from d'Ocagne's Identity:

F_2n = (F_n+1)^2 - (F_n-1)^2

w/ proof here

Noted along the way is the remarkable Cassini's Identity:

F_n-1 F_n+1 - (F_n)^2 = (-1)^n

Edited on May 6, 2021, 9:40 pm

Posted by Steven Lord on 2021-05-06 21:34:18

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