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Q: Does the limit exist for fn divided by fn-1 in the Fibonacci sequence and if so what is it?

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If a monotone sequence An is convergent, then a limit exists for it. On the other hand, if the sequence is divergent, then a limit does not exist.

The limit of the ratio is the Golden ratio, or [1 + sqrt(5)]/2

55 is the largest triangular number in the Fibonacci sequence. 55 is a popular speed limit 55 is a odd

Yes, it does.

In a Fibonacci sequence, sum of two successive terms gives the third term.... here is the Fibonacci sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144........ General formula to generate a Fibonacci sequence is """Fn= Fn-1 + Fn-2""" To check whether a number is Fibonacci or not follow the following steps: 1) Get the number as input from user. 2) Fix the first two numbers of sequence as 0 and 1. 3) put a sentinel loop with upper limit being the input number. 4)in the body of loop generate the next number in sequence in each iteration and continue swapping the values as follows: a=0 b=1 next=a+b while (next< input) a=b b=next next=a+b wend 5) lastly when program exits the loop compare the last number of sequence with the input number if they are equal then number is Fibonacci otherwise not. otherwise the last term of sequence will be less than the input number.

No, such a sequence is not posible.

Wrong answer above. A limit is not the same thing as a limit point. A limit of a sequence is a limit point but not vice versa. Every bounded sequence does have at least one limit point. This is one of the versions of the Bolzano-Weierstrass theorem for sequences. The sequence {(-1)^n} actually has two limit points, -1 and 1, but no limit.

History has it that Fibonacci was a great mathematician who, in the thirteenth century, was involved in a mathematical competitions. In one of these competitions he was given the problem of how fast rabbits would breed under ideal circumstances. The problem set the limit of each pair giving birth to just two offspring, and none of the rabbits die. In the process of solving the problem, the sequence of numbers now called the Fibonacci Sequence was proposed. The sequence begins with 0, 1 and the sequence of new numbers is the sum of the previous two numbers. Thus we have the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc. This sequence has also been determined to approximately represent many facets of nature, for example the manner in which a trees branches form, the formation of a delta at a rivers end, efc. - wjs1632 -

The limit of Fn/Fn-1 (where Fn is the nth member of the sequence) as n approaches infinity is the golden ratio, approximately 1.62:1. The Parthenon was constructed using this ratio for things like the length to height as it is the ratio at which things appear most attractive to the eye.

The "golden ratio" is the limit of the ratio between consecutive terms of the Fibonacci series. That means that when you take two consecutive terms out of your Fibonacci series and divide them, the quotient is near the golden ratio, and the longer the piece of the Fibonacci series is that you use, the nearer the quotient is. The Fibonacci series has the property that it converges quickly, so even if you only look at the quotient of, say, the 9th and 10th terms, you're already going to be darn close. The exact value of the golden ratio is [1 + sqrt(5)]/2

Students surely can recognize the number that is the limit of this sequence.

#include<stdio.h> #include<conio.h> void main() { int a=-1,b=1,c=0,i,n; clrscr() printf("Enter the limit"); scanf(%d,&n) printf(the resultant fibonacci sequence is:) for(i=1;i<=n;i++) { c=a+b; printf(%d, c) a=b; b=c; } getch(); }

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