Sequence Definition and 1000 Threads

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 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 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...

[SIZE="4"]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

Homework Statement Find the limit of the sequence \lim n\rightarrow \infty \frac{e^n+3^n}{5^n} Homework Equations The Attempt at a Solution L'Hopital's rule never ends with this one. But even after taking the first derivative of the top and bottom it shows that 5x will always be grower...

I know about the proof using lim inf and lim sup and the proof using a convergent subsequent, however I thought about this proof. Can you tell me if it is correct, and if not why? Thank you let Sn be Cauchy seq in R Let S be its range. Then S is bounded. Since R is complete, sup...

Homework Statement Find the general term of the sequence, starting with n=1, determine whether the sequence converges, and if so find its limit. (a) {(1/2), (3/4), (5/6), (7/8), ...} (b) {(1-(1/2), ((1/3)-(1/2)), ((1/3)-(1/4)), ((1/5)-(1/4)),...} Homework Equations My text only...

Homework Statement Hello! I'm having some trouble trying to understand basic concepts of Convex Analysis (I study it independently). In particular, I have a book (Convex Analysis and Optimization - Bertsekas) which gives a definition for the convergence of a sequence of sets: Homework...

(23)/(24), (11)/(12), (21)/(24),(5)/(6), (19)/(24), (3)/(4)

I don't speak English very well, so it's very hard to me to explain my attemps to solve this problem, and I'm still learning to use latex, so it's so slow to me. I can scan my attemps if you want to see them. Homework Statement I_n = \int_{0}^{\infty} x^{2n-1}/(x^2+1)^{n+3} \dx, n \geq 1 I...

Can someone explain to me what is this sequence referred in the page? http://oeis.org/A004730"

Homework Statement Can someone explain to me what is this sequence referred in the page? http://oeis.org/A004730"

Homework Statement Prove that if the sequence {An} converges to A, then the sequence {|An|} converges to |A|. And is the converse true? This is for my calculus class and it needs to be in proof format. Thank you! The Attempt at a Solution I'm totally lost, I was going to use ||x| -...

Homework Statement Determine the limit of the sequence (n^n)/(n!) Homework Equations The Attempt at a Solution I think the limit should be infinity as n^n grows faster than n!, but I'm not sure how to prove it. Thanks for the help!

Homework Statement Determine whether the sequence converges or diverges. If it converges, find the limit. an = e1/n Homework Equations The limit laws, adapted for sequences. The Attempt at a Solution I have the solution; I was just wondering if someone might explain it to me. I...

If some (sequence)^2 converges does that mean the original (sequence) always converges? (using mobile version) attempted solution: All i know is if {an} converges to L==> {an}^2 converges to L^2

Dear friends can you show me please an example of a sequence of integrable functions fn:R->R converging to an integrable function f but *not* in the L1-norm, i.e. such that \Int \mid f_n -f\mid is not equal to 0? Thank u a lot

Homework Statement show if has a uniform convergence of pointwise also we know that x gets values from 0 to 1The Attempt at a Solution for the pointwise I think its easy to show that limfn(x) as n->infinity is 0 but I am really stuck in uniform convergence I know that fn converges...

Homework Statement Assume the sequence \{ a_n \} satisfys 0 < a_1 < 1 and a_{n + 1} = a_n (1 - a_n )(n \ge 1) ,prove \mathop {\lim }\limits_{n \to \infty } {\kern 1pt} {\kern 1pt} {\kern 1pt} na_n = 1 Homework Equations The Attempt at a...

Ok so for a sequence x(n) to be bounded it means |x(n)|<=M but according to by book, if x(n) belongs to some closed interval, say [a,b], x(n) is bounded. That is confusing because say x(n) belonging to [a,b] means a<=x(n)<=b. How can there exist a M such that -M<=x(n)<=M? this means...

Given f1+f3+f5+...+f2n-1 = f2n. Prove by induction. So using the general Fibonacci sequence formula, Fn=Fn-1 + Fn-2 , I got f1+f3+...+f2n+1 = f2n+2 then using the formula, f1+f3+...+f2n+1 +f2n = f2n+2. This ends up giving me, f2n + f2n does not equal f2n+2. What's wrong here? (...

I'm having trouble with a word problem: The people of Gossipopolis cannot keep a secret. Upon being told a secret, a person from Gossipopolis will spend the next hour telling three people. In turn, those friends will spend the next hour each telling 3 more people. This process continues and...

I'm a little stuck here... I need to write this in the summation notation, and then find and prove a formula in terms of n, using induction :3+7+11+...+(4n-1) I know that the summation notation is n +--- \ / 4i-1 +--- i=1 but I have no idea how to...

Homework Statement Let an = ( 1 + \frac{1}{n} )n Homework Equations show that if 0 <= a < b \frac{b n+1 - a n+1}{b-1} < (n+1)bn The Attempt at a Solution I have started from a < b and I said so an < bn Then I multiply by (n+1) So I get the left hand side...