# seq

1. ### Fibonacci Seq bit string proof. Show that pattern can't have three consecutive 1s

I'm having a little trouble figuring out how to prove this. So, the sequence is as follows: S0 = 0 S1 = 1 S(n-2)S(n-1) for all n >= 2 That means S2 = 10 S3 = 101 S4 = 10110 S5 = 10110101 Now the question that I'm stuck on is: Prove that the pattern can't have three consecutive ones...
2. ### Maple versus matlab in seq and series'

I solved a 2nd degree taylor polynomial using Matlab and checked it in Maple: The function f (x) was: => x * e ^ x, at a = -1 Maple gives me Tn(x) = -1/e+.... I do not wish to write it all out here but will state that it give me ln If I do the same using Matlab, it gives me the same answer...
3. ### Seq help!

Let S be the sum of the 1st 120 terms of an arithmetic progressio with first term a and common difference d. Given that the 9th term is -14 and the sum of the first 40 even-numbered terms is S/6 -780 , find the value of d. Help I dont now how to attempt the part on 1st 40 even no. I would...
4. ### Proving convergent seq. is a cauchy seq.

I proved convergent sequences and cauchy sequences. How would I prove that every convergent sequence is a Cauchy sequence?
5. ### contractive seq

let \ x_1>0 \ , \ x_{n+1}= \frac{1}{2+x_n} \ n \in N . prove \ that \ x_n \ is \ a \ contractive \ sequence . what \ is \ its \ limit \ ?
6. ### Any bounded seq. has a converging subseq. <=> every bounded monotone seq. converges

How would I go about proving such a statement? Any help would be great thanks.
7. ### Prove every unbounded seq. contains a monotone subseq. that diverges to infinity

Could anyone explain to me how I would go about proving such a statement? Thank you and good day.
8. ### "Interesting" connection between prime numbers and the fib seq. Pls critique

I have stumbled upon a weird connection between the fibonacci sequence and prime numbers which I'd like to share with you for critique. It may well have been discovered before or be a simple extension to already known theories but I'd thought I'd throw it out here and see if anyone can help me...
9. ### Cont. Func + Cauchy Seq

Give an example of the case or explain why it's not possible for each of the following: 1.) Continuous function f : (0,1) \rightarrow \mathbb{R} and also a Cauchy sequence (x_n) such that f(x_n) is not a Cauchy sequence. 2.) Continuous function f : [0,1] \rightarrow \mathbb{R} and also a...
10. ### arithmetic seq. !

please help ! Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence? Give at least two real-life examples of a...