Sequence Definition and 1000 Threads

I have 4 problems left and the questions says I have to test them for converge or divergence. Here are the problems http://gyazo.com/f0fa5a38c5968ecb7e74103486a181bd.png http://gyazo.com/4689f9d02d0b264c2c2b64ff4907ba77.png for 25, I want to take the limit as n goes to infinity however I get...

The sqeuence of ratios of a fabinacci number F_n+1/F_n on looking at this. F_2/F_1 =1/1 =1 F_3/F_2 =2/1 =2 F_4/F_3 =3/2 =1.5 F_5/F_4 = 5/3 = 1.667 Why would F_n+1 = at F_4 =3 with also F_3=2 I think i understand the squence is fabin accie on the denominater but on the...

Homework Statement Ok here is the problem: 100 loaves of bread are to be distributed such that the quantities form an arithmetric sequence, among 5 people. The first 2 together receive 1/7 of the remaining 3, together. How much (loaves and fractions) does each receive? Homework...

Homework Statement Suppose \Omega is an infinite set. If Q = \{x_1,x_2,...\} \subset \Omega is infinite and countable, and if B_n := \{x_1,x_2,...,x_n\}, A_n := Q - B_n , ... does A_n \downarrow \emptyset? If \mu is the counting measure on \Omega, is \lim_{n \to \infty} \mu (A_n) = 0?The...

Let's say an extraterrestrial space probe crashes into Earth and we recover from it a disk that we conclude contains a genome. Would we be able to tell anything about them from that information alone? What kind of experiments would you run on it?

I have observed a strange thing when you modify a sequence of numbers bit by bit.

For these four practice problems, I had little idea what the hell to do (plugging in seemed worthless), could anyone help? Sorry if this isn't what the board is suppose to be used for. Answers in spoiler tags. If k and h are constants and x2+kx+7 is equivalent to (x+1)(x+h), what is the value...

Homework Statement Would tau and phi be considered conjugates? Homework Equations \tau = \frac{1-\sqrt{5}}{2} \phi = \frac{1+\sqrt{5}}{2} The Attempt at a Solution I know that a complex number such as 1+2i would have 1-2i as a conjugate. However, for fractions, I can't quite remember if the...

Homework Statement Determine the convergence or divergence of an = np / en The Attempt at a Solution Using L'Hopitals Rule, I get (p(nP-1en) - nPen) / e2n which, if I take the limit as n \rightarrow\infty I still get \infty/\infty which doesn't help. I can see if a sequence...

i know how the basic geometric sequence system works, but what if i want to subtract a fixed amount every For example if i start with $5000 (a1) and is multiplied by 1.05 (5% / r) every day for 20 days (n) I would have $13,267. But what would I have if $20 dollars was subtracted from the...

Given N= 1.2.3 + 2.3.4 + ... + n(n+1)(n+2), prove that 4N + 1 is a square (n is a positive integer)

I'm looking for a convergent sequence s_n such that: lim_{n\rightarrow\infty}n(s_n-s_{n-1})=\infty I've already gone pretty far afield in my hunt for such a sequence, so I thought I'd enlist the help of you fine folks in my search.

Hi. I found some rational sequences that converge to irrational limits, but am not having any luck going the other direction, i.e., an irrational sequence that converges to a rational limit. Any suggestions?

I have a question regarding the following definition of convergence on manifold: Let M be a manifold with atlas A. A sequence of points \{x_i \in M\} converges to x\in M if there exists a chart (U_i,\phi_i) with an integer N such that x\in U_i and for all k>N,x_i\in U_i \phi_i(x_k)_{k>N}...

So for those of you who don't have the book the problem goes like this: Fix a > 1, take x_1 > sqrt(a), and define: x_{n+1}=\frac{a+x_n}{1+x_n}=x_n+\frac{a-x_n^{2}}{1+x_n} a) Prove that x_1 > x_3 > x_5 > ... b) Prove that x_2 < x_4 < x_6 < ... Basically my strategy is to show that the...

I was wondering whether a sequence like x_n=n\sin n converges* to infinity or diverges. I'm pretty sure it goes to infinity but it still oscillates. *Let's say we are in the extended real number system where we can converge to infinity EDIT: I mean x_n=n+\sin n

I've constructed a visualisation of the solution of an equation over time as a sequence of MatrixPlots and I'd like to export this as a movie for use in a presentation, but whatever file extension I try, I either get an error message (e.g. "The Export element \!\(\"GraphicsList\"\) contains...

Homework Statement If the absolute value of a sequence, an converges to absolute value of A, does sequence, an necessarily converge to A? Homework Equations convergence: a sequence { an}n=1-->infinity, converges to A є R (A is called the limit of the sequence) iff for all є > 0, there...

Hello there guys, I'm new on this forum so nice to meet you all! By the way, i am thinking about writing your own nucleotide sequence codons for a DNA/RNA/Gene/Genome/Chromosome for my Synthetic Life Simulation which allows the user to evolve from a simple cell to a complete organism via user's...

Sorry, I got it.

There are two space stations A and B which are at rest wrt to each other and separated by some distance x. Each space station has a light that randomly flashes. I am in a third space station, somewhere in the middle of A and B and at rest wrt to the other two stations. I see Station A’s...

Homework Statement Let \{ f_{n} \}_{n=1}^{\infty} \subset C[0,1] be twice differentiable, and satisfying 0 = f_{n}(0) = f'_{n}(0) and \| f''_{n}\|_{\infty } . Prove that \{ f_{n} \}_{n=1}^{\infty} has a convergent subsequence. Homework Equations So since C[0,1] is a compact metric...

Homework Statement Prove that every convergent sequence is bounded. Homework Equations Definition of \lim_{n \to +\infty} a_n = L \forall \epsilon > 0, \exists k \in \mathbb{R} \; s.t \; \forall n \in \mathbb{N}, n \geq k, \; |a_n - L| < \epsilon Definition of a bounded sequence: A...

Homework Statement Problem 1: Two Arithmetic Sequences are given. a_n = 200,196,192,188,184... [ltaex]b_n = 100,103,106,109,112...[/itex] For integers l,m, find the number of pairs consisting of (l,m) which satifies condition a_l = b_m Problem 2: Three terms, sin(x)...

I know this problem probably extremely easy, and I can see the pattern of the sequence but I can't seem to figure out how to represent that pattern as an equation. The sequence is 1-1/2+1/6-1/24+1/120... Now I obviously see that to get the next term you multiply the previous term by 1/n but...

Homework Statement Let {M_i} be an orthogonal sequence of complete subspaces of a pre-Hilbert space V, and let P_i be the orthogonal projection on M_i. Prove that {P_i(e)} is Cauchy for any e in V 2. The attempt at a solution I'm trying to prove as n and m goes infinity...

Homework Statement show that (the range of) a sequence of points in a metric space is in general not a closed set. Show that it may be a closed set. 2. The attempt at a solution I don't know where to start. For example, if we are given a sequence of real numbers and the distance...

Homework Statement (This is my first post and I'm not sure why the Tex code isn't working, sorry).Suppose fis a positive continuous function on [1,0] .For each natural numbern define a new functionF_n s.t. F_n(x) = \int_0^1 t^ne^{xn}f(t)dt (a) Prove that lim_{n\to\infty}F_n(x) = 0 for...

I want somebody to help me what attempts have been made to understand the sequence of prime number. Is the Nth term of the sequence disclosed?

Homework Statement Use bernouillis inequality to show that \stackrel{lim}{_{n \rightarrow \infty}} (\frac{1+\frac{x+y}{n}}{1+\frac{x+y}{n}+\frac{xy}{n^{2}}})^{n}=1 x,y \in R Homework Equations The Attempt at a Solution With simple manipulation this equals: \stackrel{lim}{_{n \rightarrow...

I was thinking of how ( 1 + (1/n) ) ^ n converges to e and I am aware of how if it is raised to some an, then it converges to e^a. If i recall if the form ( 1 + (a/n) ) ^ n converges to ae? I was hoping someone could tell me how to deal with ( 1 + (1/n^2) ) ^ n? Thanks!

Does anyone have a DIRECT proof of the relationship between Pascal Triangle and Fibonacci Sequence? I mean not like induction or other method of proof but a direct method. I try to google it but couldn't find one

Homework Statement {xn} is an infinite sequence and xi ≠ xj if i ≠j. Let A and B denote all finite subsequences of {xn} and all infinite subsequences of {xn}, respectively. (a) Show that A is countable. (b) Show that B ≈ (0,1). Homework Equations The Attempt at a...

Homework Statement Let (x_n) be a real sequence which satisfies |x_n - x_(n+1)| < (1/n) for all natural numbers n. Does (x_n) necessarily converge? Prove or provide counterexample. Homework Equations Cauchy Criterion for sequences The Attempt at a Solution I figured at first...

Homework Statement [PLAIN]http://webwork2.math.utah.edu/webwork2_files/tmp/equations/a4/32b370a8c66b49443277f94aa0edf51.png Homework Equations The equations that I can see in my book and online look nothing like this problem. The Attempt at a Solution Really just looking for a pointer in...

A ball is dropped from a height of 3 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen. (a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. (Enter your answer as an improper fraction.) Can...

Hello everyone, :smile: I was working to create a program to list the sequence: 1 12 123 1234 12345 ... The user will decides how many terms of sequence are displayed. For example the terms, n, given above are five. Will you help me please? I think I need to use the FOR loop here...

Homework Statement A lot of my homework asks me to determine if a given matrix (sequence of vectors) is a basis or not. Homework Equations The Attempt at a Solution Can I just find the reduced echelon form of a given matrix and see if it is linear independent or linear...

Hello Friends, I am at a loss to understand a proof concerning the proof of divergence of (-1) ^n sequence. According to the book: "To prove analytically that the sequence is convergent, it must satisfy both of the following conditions: A: |-1-L| < epsilon B: |+1 - L| < epsilon " (+1...

!Showing a sequence is less than another sequence (sequences and series question) Homework Statement [PLAIN]http://img263.imageshack.us/img263/385/sandq1.gif Homework Equations The Attempt at a Solution i re arranged the equation and wrote in terms of an to get an=-4an+1/an+1-7 and an+1...

In a geometric sequence, the sum of the first three terms is 7 and the sum of the cubes of the first three terms is 73 find the sequence and how did you get it

Homework Statement Write the following expression in a simpler form: $\sum_{1}^{n} F_{2i} \cdot F_{2i-1}$ It doesn't have to be closed-form, probably something on the line of: $\sum_{0}^{n} F_{i}^{2} = F_{n} \cdot F_{n+1}$ (We define the sequence the ususal way, starting the indexing from 0...

I am very new with Mathematica and I need help writing a program that generates a Farey Sequence. Farey[n] := ? The result should appear as follows, for those values of N. Farey[1] = {0/1,1/1} Farey[2] = {0/1,1/2,1/1} Farey[3] = {0/1,1/3,1/2,2/3,1/1} Farey[4] =...

Here is an overview of Farey sequences; http://mathworld.wolfram.com/FareySequence.html" I need to write a program in Mathematica 8, FareySequence[n_], that takes a positive integer n and returns, as a list, the nth Farey sequence. So far I have, Module[{denleft, denright, f, i, j, k...

I am stumped! What numbers follow this sequence what what is the formula?? 2 0 2 0 3 3 2 4 Thank you!

I need some help writing a Farey Sequence in Mathematica, so far this is all I have: FareySequence[n_] := GCD[a, b]; While b : a, b = b, a % b; result := a Simplify[a, b]; g := GCD[a, b] result := (a/g, b/g) I am very new to programming, please help!

The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.35 rad/s2. It accelerates for 33.9 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 51.1 s after it begins rotating. α = 1.35 rad/s^2...

can someone help me determine whether this sequence is periodic? [cos((2pi/3)n + pi/6) + 2sin((pi/4)n)] where n is all integers i know that for a function to be periodic, x(n) = x(n+N) however, i am confused because both the cos and sin component contain n please help. thx.

I attended a talk where a physicist mentioned this sequence from n=1 to infinity and apparently the answer is -1/12? Could someone explain please?

Hi! I'm reading a book on the finite element method and the author mentions a free and total sequence in a hilbert space. I've been searching the internet, but I just can't find the definition of a free sequence. Does anybody know what it is? Thanks in advance