Sequence Definition and 1000 Threads

Homework Statement Two consecutive numbers from 1,2,3...n are removed A.M of remaining numbers is 105/4. Find n and those numbers removed .Homework Equations Answer n = 50 those numbers are 7 and 8 The Attempt at a Solution I solved this question like a few weeks ago but now it escaped my...

I asked this question before but I totally misunderstood what it was asking. Basically, I need to find that there exists a sequence {a_k} such that it converges to x for some x in R. Since the real numbers are equivalence classes of convergent Cauchy sequences the result seems fairly obvious...

Homework Statement Calculate the energy generation coefficient ε (J s^-s kg^-1) in the center of a 50 Solar mass Main Sequence star, assuming that all luminosity is generated in a constant density core containing one tenth of the total mass of the star. Homework Equations L=M^3.3...

Hello was wondering if anyone could help me prove that: Suppose (sn) converges to s not equal to 0 and ( sntn) converges to L. Prove that (tn) converges

If 0<r<1 and |x(n+1) - x(n)| < r ^n for all n. Show that x(n) is Cauchy sequence. help please.

I've been trying to learn some maths by myself. A book I found starts with a section on limits. I feel that I have a decent understanding of what is written, but then, there are some problems given that I just can't figure out. I feel like I'm missing something basic. I'm not sure what I'm...

Im struggling with the concept of this basic sequence question. Let x(n) be a sequence such that lim(n->00) (nx(n)) = 0 i.e. it converges to zero... How could i show that there is an N s.t. for all n≥N : -1 < nx(n) < 1 Any tips would be great.. I don't want an answer.. I want to...

I finished exploring a family of functions fk(x) = {xksin(1/x) for x≠0 {0 for x=0 for an assignment in my Analysis course, and I'm supposed to determine the highest order derivative that exists and whether or not it's continuous...

Simple question just as the title says, but I can't remember or derive the solution for the life of me. I know that the answer is 0. I know why the answer is 0. But I need to know the mathematical derivation of the solution, and that's the part that I can't remember. So, to reiterate, how do you...

Homework Statement Show that 2^{n^{1001}} |a_{n} - a_{\infty}| \rightarrow 0 as n \rightarrow \infty. Here, an is defined recursively by a_{1} = 1, a_{n+1} = \frac{1}{2}(a_{n}+\frac{x}{a_{n}}). I already know that a_{\infty} = \sqrt{x}.Homework Equations We are given a hint to consider...

Homework Statement 5^2 - 5^3 + 5^4 - ... + (-1)^k*5^k whre k is an integer with k >= 2 Homework Equations The Attempt at a Solution I know (5^(k-1) - 5^2)/2 gives you the sum if they were all positive. I tried multiplying it by (-1)^k or something but that just changes the sign. I...

Homework Statement The following series is a telescopic series. Find the exact sum of the series by performing a partial fraction decomposition and generalizing the formula for the nth partial sum Sn. Homework Equations The Attempt at a Solution 3n + 2 = A(n+1)(n+2) + B(n)(n+2) + C(n)(n+1)...

[PLAIN]http://img805.imageshack.us/img805/1575/photo0138d.jpg Hi, on thursday, i have exam of advance calculus and i could not solve two problem in study sheet given by İnstructor. By 9 question, i prove by add an subtract XnY to |XnYn-XY| and i have found that |Xn(Yn-Y)+...

Homework Statement Use the definition of a limit to prove that lim [(1+an)-1] = 1/2 if lim an = 1. Homework Equations (\forall\epsilon>0)(\existsN\inN)(n\geqN \Rightarrow|an-L|<\epsilon) The Attempt at a Solution Let \epsilon be arbitrary. Since lim an exists, \existsN\inN such...

Since I don't know how to use latex I have posed my question in word file. Yours help is greatly appreciated.

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 I'm having trouble understanding dynamic programming as it relates to sequence alignments. I understand from my lecture notes that the scoring matrix used has arbitrary values (in our case +5 for match, -2 for mismatch, and -6 for gap). I therefore understand why square...

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. :(

Hello! Homework Statement As the title says I am attempting to calculate the mass displacement of a motion capture sequence, however I am not seeing the results I expect which is why I am posting here to make sure I have understood everything correctly. The data that is known is the...

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

Hi. When we say that \displaystyle \lim_{n \to \infty}f_n(x)=g(x), do we mean that f_n is pointwise or uniformly convergent to g? Thanks.

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...