Answer to Question #120775 in Wolfram Mathematica for Nina

Question #120775
Is the Fibonnaci sequence rising faster than the exponential function?
1
Expert's answer
2020-06-08T16:43:05-0400

Let be the Fibonacci number.

We will prove by strong mathematical induction that

Base case:

Induction step:

Assume for all , then

So, the inequality is true for , thus, by strong mathematical induction for all and

Hence


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