Table of Contents

## Is the limit of Fibonacci a 9?

The ratio of successive Fibonacci numbers converges on phi

Sequence in the sequence | Resulting Fibonacci number (the sum of the two numbers before it) | Ratio of each number to the one before it (this estimates phi) |
---|---|---|

7 | 13 | 1.625000000000000 |

8 | 21 | 1.615384615384615 |

9 | 34 | 1.619047619047619 |

10 | 55 | 1.617647058823529 |

## What is the sum of fib 10 )+ fib 5?

the tenth Fibonacci number is Fib(10) = 55. The sum of its digits is 5+5 or 10 and that is also the index number of 55 (10-th in the list of Fibonacci numbers).

**What is the 38th term of the Fibonacci sequence?**

list of Fibonacci numbers

n | f(n) |
---|---|

36 | 14930352 |

37 | 24157817 |

38 | 39088169 |

39 | 63245986 |

**What are the 9th and 10th terms of the Fibonacci sequence?**

The 9th and 10th terms in the sequence are 21 and 34. Thus, the 12th and the 13th Fibonacci numbers are 89 and 144 respectively.

### What are the Fibonacci numbers?

In Maths, the Fibonacci numbers are the numbers ordered in a distinct Fibonacci sequence. These numbers were introduced to represent the positive numbers in a sequence, which follows a defined pattern. The list of the numbers in Fibonacci series is represented by the recurrence relation: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ……..,∞.

### How to prove the Fibonacci sequence is the sum of all?

the Fibonacci sequence. To prove the proposition, we need simply to show that the sum of all numbers in the (n 2) nd diagonal and the (n 1) st diagonal will be equal to the sum of all

**What are the similarities between Lucas numbers and Fibonacci numbers?**

Fibonacci numbers are also closely related to Lucas numbers L n {displaystyle L_{n}} in that they form a complementary pair of Lucas sequences U n ( 1 , − 1 ) = F n {displaystyle U_{n}(1,-1)=F_{n}} and V n ( 1 , − 1 ) = L n {displaystyle V_{n}(1,-1)=L_{n}} . Lucas numbers are also intimately connected with the golden ratio.

**What is the smallest Fibonacci number that has a prime factorization?**

The smallest Fibonacci number which has the n th prime as a factor gives the series: 2, 3, 5, 21, 55, 13, 34, 2584, which is A051694. But as these Fibonacci numbers get large rapidly, it is easier to use the index numbers of such Fibonacci numbers to get the series above (A001602).