Question

100pts: As the value of n increases, what famous ratio is approached by the ratio between the nth Fibonacci number and the (n-1)th Fibonacci number?

Answer 1

Answer:

The Golden ratio, phi

Step-by-step explanation:

A fibonacci series is one in which the next term is equal to the sum of the previous two terms.

0,1,1,2,3,5,8..

When you take the ratio of these terms:

3/2 = 1.5

5/3 = 1.666666667

8/5 = 1.6

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As you increase the no. of terms, you'll observe that this ratio approaches 1.618 (ph, The Golden ratio)

Answer 2

Two successive Fibonacci Numbers, their ratio is very close to the Golden Ratio which equals approximately 1.618034