Sequence Definition and 1000 Threads

Does it look like he wants a rough demonstrative "proof" involving plugging in xn = (sn) or rather, say, an epsilon-N proof? http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled-1.png?t=

Hi there, I am working on a problem about a combination of some items. The data set consists of three different sets. The first set are all combinations of six numbers from {0, 1, 2, 3, ..., 10, 11, 12}. The second set are all combinations of two numbers from {13, 14, 15, 16, ..., 24, 25}...

Homework Statement What is the fastest way to prove this. 1/an→1/a, where an is a sequence. The attempt at a solution I know how to prove this but I am looking for a simple and elegant proof.

So the problem is here: https://www.physicsforums.com/showthread.php?p=3532161&posted=1#post3532161 And I understand the answer and all, but I want to go further. MATLAB will be main tool for upcoming years so I have to learn. I want to plot this: \sum 2^{i}= 500 000 where sum goes from...

Consider the sequence (n) n=1 to infinity. Plot the sequence on the unit circle: n modulo 2*pi for n≥1. What do you see? Attempt: I really honestly have no idea what to do. We are learning in class about limit laws and how to prove them, so this question seems to be coming out of nowhere. :(

I have this question asking what the mRNA sequence would be. 5'-ATGATATCAAGCACACACGCAACGTGCGAATTACTATAG-3' 3'-TACTATAGTTCGTGTGTGCGTTGCACGCTTAATGATATC-5' I'm confused about what I am doing wrong. Isn't the open reading frame AUG so you would read it to be AUG AUA UCA AGC ACA CAC GCA...

This sequence is stumping me, how would I go about solving this? Write the sequence B = 1, -1/2, +1/4, -1/8, +1/16, ... in closed-form. I tried using (-1) has the top with different variable son the bottom, but nothing seems to add up. The 1 in the front is throwing me off. Any help would be...

Hi! While studying sequence and series, I've gotten some misunderstandings in the definitions of sequence and series. What I know about the definitions of sequence and series is as follows below ; a sequence of field of real numbers is defined as a function mapping of the set of all positive...

Homework Statement prove that the series summation from n=3 to infinity of (1/(n*log(n)*(log(log(n))^p)) diverges if 0<p<=1 and converges for p>1. Homework Equations The Attempt at a Solution 2^n*a(2^n)= 1/(log(2^n)*(log(log(2^n))^p)). this is similar to the summation from n=2 to...

How do I evaluate lim n->inf 3^n/(3^n + 2^n) l hospitals rule (or however you spell his last name lol) doesn't work and so I have a hard time proving that it equals one. Thanks for any help anyone can provide.

What is the main reason why there are so many more stars in the Main sequence in comparison with the number of red giants?

Hey all, University for me started last week, however I was unable to attend until now. I just e-mailed my professor and there is a quiz just next week and I have no notes and he will not give them to me. I'm wondering if anyone knows any good online sites that could help me catch up. Here...

Homework Statement I have to find the order of convergence of the following sequence b_n = \left( \frac{5}{6} \right)^{n^2} I have numerically tested that it has to be a real number between 1 and 2, but I can't find it exactly. I also have this doubt: does every sequence have an...

I think I'm not understanding something here: A point L \in \mathbb{R} is a limit point of a sequence a_n if exists a subsequence b_n such that \lim b_n = L So for example the constant sequence a_n = 1 so that a = 1, 1, 1, 1, 1, 1, \ldots has a unique limit point L=1 But a limit point...

Homework Statement A bounded sequence need not be convergent Can you show me an illustration which shows a sequence that is convergent? I don't understand when if lim n ---> infinity sn = l, the sequence sn converges to l or {sn}. Now what is l ? My attempt or understanding of the...

Homework Statement show that holds, \sum\limits_{n=1}^{\infty}\int\limits_{0}^{\frac{\pi}{2}}\frac{(2n-1) sin(2n-1) x}{n^2(n+1)}dx = \sum\limits_{n=2}^{\infty}\frac{1}{n^2} Homework Equations The Attempt at a Solution Actually, I have no idea how should I start.

Let A and B be two coprime integers. Find X = zero mod A such that Y = 2*X +1 = 0 mod B. Then 8*(Y +2*N*A*B)*(X + N*A*B) + 1 is a square for all integer N. If A = 5,B = 7, X = 10, Z = 21 then the sequence of square roots of the Squares for N = -3 to 3 is -379, -249, -99, 41, 181, and 321. Of...

Homework Statement let (Xn) be a sequence in R. Let (An) be a sequence defined as An=(X1 +X2+...Xn-1+Xn)/n. (Xn) is a convergent sequence and the limit of Xn as n goes to infinity is L. Prove (An) in convergent sequence and that the limit is also L. Homework Equations The Attempt at...

Homework Statement let (Xn) be a sequence in R given by X1=1 and Xn+1=1/(3+Xn) for n>=2. prove Xn converges and find the limit. Homework Equations The Attempt at a Solution well i think using the monotone convergence theorem would help but i would have to prove that the sequence...

Hi, Just hoping someone could check my work and point out any errors, if any. Homework Statement Consider the sequence {a_n} defined by a_n=\frac{n}{2n+\sqrt{n}}. Prove that \lim_{x\to\infty}a_n=\frac{1}{2}. (Do NOT use any of the "limit rules" from Section 2.2.) Homework Equations A...

Let f_{n} be the Fibonacci sequence and let x_{n} = f_{n+1}/f_{n}. Given that lim(x_{n})=L exist determine L. Ok so I know that the limit is \frac{1+\sqrt{5}}{2} from previous experience with the sequence, but I am not sure how do you show that without writing out a lot of terms and then...

If (b_{n}) is a bounded sequence ad lim(a_{n})=0 show that lim(a_{n}b_{b}) =0 Pf/ Let b_{n} be bounded and the lim(a_{n})=0. Since b_{n} is bounded we know that \exists a real number M \ni |b_{n}|<M for all n\inN and we also know that |a_{n}|< \epsilon for all \epsilon>0.My problem is how do I...

use the definition of a sequence to establish the limit lim(\frac{2n}{n+1})=2 Let \epsilon>0, then |\frac{2n}{n+1}-2| <\epsilon. Next we have that | \frac{2n-2n+-2}{n+1}|= |\frac{-2}{n+1}| <\frac{2}{n}. So \exists k\inN such that \frac{2}{k}<\epsilon. When n\geqk, we have \frac{2}{n} <...

Call {a1, a2, a3, ...} = {an} a "convergent sequence" if \exists L \in \mathbb{R} : \quad \forall \epsilon > 0 \quad \exists N \in \mathbb{N} : (\forall n > N \quad (n > N \implies |a_n - L| < \epsilon)) in which case we write \lim_{n \rightarrow \infty} a_n = \lim a_n = L. Of course this...

Homework Statement Find the limit of n^2(e^\frac{1}{n^2} - cos(\frac{1}{n})) Homework Equations The Attempt at a Solution since cos(1/n) is asymptotic to 1. n^2(e^\frac{1}{n^2} - cos(\frac{1}{n})) ~ n^2(e^\frac{1}{n^2} - 1) ~ n^2 \frac{1}{n^2}) = 1 The right answer is 3/2...

I like to plan ahead so as of now I basically have a good idea what my schedule will be like for all 4 year of college. I want to go into QFT eventually so I think the math classes I have decided to take will be best for that. They are Multivariable calculus( freshmen year 1st semester) Half a...

I have a sequence {xn} defined by xn = 1/n[1 + 1/2 + 1/3 + ... + 1/n] for all natural numbers n. I want to show that this sequence converges to 0, i.e. given any positive real number 'r', I want to show that there exists a natural number k such that xk < r. (The sequence is...

What do you think? http://www.amnh.org/nationalcenter/youngnaturalistawards/2011/images/aidan_large_08.jpg http://ca.news.yahoo.com/blogs/good-news/teen-aidan-dwyer-uses-fibonacci-sequence-solar-energy-182220725.html

Ok so the ideea of the proble is the following.F:A->B...where A={1...k} and B={1...n}.The problme is divided in 2 parts. The first part of the problem asked me to write in terms of k and n the formulas for the number of functions,number of injective functions,number of increasing...

Hello everyone, I will be attending OSU starting in the winter as a transfer student. I have been looking to do honors math there and just maybe double major in computer science if possible. I will have already taken calculus I + II at a four year institute which I myself might say is...

The sequence is 1,2,3,4,5,8,7,16,9 I am absolutely stumped and cannot fathom the answer. Normally I can see the logic, can anyone help with the rule? Thank you

Homework Statement This is problem 2.4.11 from Thomson, Bruckner, and Bruckner, "Elementary Real Analysis." It is from the "Challenging Problems" section of Chapter 2, Sequences. Note that differentiation and continuity have not been covered at this point, but it is presumed that the reader...

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...