Sequence Definition and 1000 Threads

Homework Statement I'm trying to find out the equation for how to find out where a number falls in a sequence. An example sequence would be 3, 9, 18, 30, 45, 63, 84, 108, 135, 165... 108 is the 8th number in that sequence. Homework Equations If I use the equation (xn+xn^2)/2 (x = 3...

Homework Statement Let x be any real number. Prove that there exists a sequence {Rn} of rationals different from x such that {Rn} converges to x. Use the Archimedian property, the fact that the rationals are dense in the reals, and the squeeze principle. Homework Equations The...

Homework Statement I want to find the limit of ƩK(n+m,n)zn K(a,b) being the binomial coefficient. Homework Equations Cauchy root test?The Attempt at a Solution Trying the cauchy root test I get: 1/R = limn->∞[(K(n+m,n))½] But what do I do from here?

Homework Statement 1) e^n / pi^(n/2) 2) (2/n)^n Homework Equations The Attempt at a Solution 1) Take out 1/pi^0.5 as a factor Now have limit of (e/pi)^n Since this ratio is less than 1, it will converge? Ooops, dw about this one, realized my mistake ^^ 2) e ^ limit ( n* ln (2/n)) e ^...

So I was trying to show that a_n = n \tan\frac{\pi}{n} is decreasing as n increases (n>=3) . I can't see it. Anyone may help ? :)

It's given in my book that from the width of spectral lines you can determine whether or not it is a main sequence star... Not sure if astro-como or quantum.. Anyway, i need a detailed easy explanation of what is the width of spectral lines.. Secondly, if we know that how will we determine...

My program needs to prompt the user to input a number, and using that number, I tell them what number in the Fibonacci sequence their input corresponds to. So the Fibonacci sequence is 0 1 1 2 3 5 8 13 So if they input the number 6, the program will return "5" as the number in the sequence...

Homework Statement Using the sandwich rule (which i understand) find the limit of n!/nn The attempt at a solution To my knowledge n! is the fastest growing function you can have, so I immediately thought the function did not have a limit, however, the answer states the limit to be 1 I know...

Hi all, What is the normal procedure to verify that I got the correct results (eigenvalues and eigen vectors) from the eigenvalue problem? I'm using the lapack library to solve eigenvalue problem summarized below. I've 2 matrices K and M and I get the negative results for eigenvalues...

http://dl.dropbox.com/u/33103477/summands.png Even with the hint, I'm confused on what to use on this ? Any ideas ?

I read in Rudin's Analysis that sequence 1/n failes to converge in the set of positive real numbers. How comes?

Homework Statement infƩn=0 cos(m*n*pi)/(n+1) where m is a fixed integer. Determine the values of m, such that the series converges. Explain your reasoning in detail. The attempt at a solution I have figured out that cos(n*pi)/(n+1) can be represented as ((-1)^(n+1))/(n+1) (as it bounces...

Homework Statement I have an image similar to the one given here with two types of material inside of it and I need to have at least one voxel in the image is entirely type B material (The smaller inside material). I am given all the dimensions on the material A and B but not told where...

Homework Statement What is the sum of: Homework Equations N/AThe Attempt at a Solution I'm unsure how to start. Note: I'm in Grade 10, so I may not have the mathematical skills necessary to understand the solutions you provide. Any help/guidance would be appreciated.

If Un+1=Un + d defines an arithmetic progression, and Un+1 = kUn defines a geometric progression, is there a name for a progression defined by Un+1 =KUn + d? Thanks.

Homework Statement Hello, I have a question concerning convergence of the non-monotonic sequences which takes place when the Cauchy criterion is satisfied. I understand that |a_n - a_m| <ε for all n,mN\ni Homework Equations What I don't see is how (a_{n+1} - a_n) →0is not...

A sequence (an) is recursively defined by a1 = 1 and an+1 =1 /(2+an ) for all n≥1 I'll prove this sequence is convergent by monoton sequence theorem.ı can find ıt is bounded but ı cannot decide it is monoton because when ı write its terms,Its terms are increasing sometimes decreasing...

Homework Statement Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequence whose values do not exceed four million...

This question is in regards to higher dimensional algebraic geometry. The actual problem is very complicated so here is my question which is substantially simplified. Suppose {f_1,... f_k} is a set of quadratic polynomials and {g_1,...,g_l} is a set of linear polynomials in a polynomial ring...

Homework Statement the sequence is an = (cos(n))^2 / 2^n Homework Equations none really The Attempt at a Solution like i mentioned in my last post, i usually use l'hopitals or dividing by the largest exponent from the denominator. here, i don't see why i would want to use...

Homework Statement A sequence {an} defined recursively by a1=1 and an+1=\frac{1}{2+a subn}, n\geq1. Show that the sequence is convergent. Homework Equations If a sequence is bdd below and decreasing or it is bdd above and increasing, then it is convergent. The Attempt at a Solution...

Homework Statement Show that for all n greater than 1: fn = \frac{1}{\sqrt{5}}{(\frac{1+\sqrt{5}}{2})n - (\frac{1-\sqrt{5}}{2})n} Homework Equations f1 = f2= 1 fn+2 = fn+1 + fn The Attempt at a Solution I'm pretty sure it's by induction, but I'm not sure how to start.

The sequence is: ((e^n) + (e^-n)) / (e^2n - 1) I don't know how to find this limit. Am I supposed to take the natural log of each term? If so you end up with: (n*ln(e) + (-n)*ln(e)) / (2n*ln(e) - ln(1)) Which all the ln(e) are just equaling 1 so it becomes: (n-n) / (2n - ln(1))...

A sequence (an) is defined recursively by a1 =1 and an+1 = 1/ 2+an for all n is greater than 1 or equal 1. ı'll prove that this sequence is convergent,buy ı cannot decide whethet it is increasing or decreasing .When ı write terms ,some terms increase some terms decrease.

If( an) convergent sequence,prove that lim n goes to infinity an = lim n goes to infinity a2n+1. I think a2n+1 is subsequence of (an ) and for this reason their limit is equal. but ı don't know where and how to start..

State whether the sequence converges as n--> ##∞##, if it does find the limit i'm having trouble with these two: n!/2n and ∫ e-x2 dx now I know they're special forms so the ordinary tricks won't work. Any help or hints?

I'd like to know how do i find I2 (Negative sequence current) if I know Ia, Ib and Ic but don't know angle (in normal system_not fault)? My system's 3 phases 3 wires.

Consider a sequence \{ a_{n} \} . If \lim_{n→∞}a_{n} = L Prove that \lim_{n→∞}a_{n-1} = L I am trying to use the Cauchy definition of a limit, but don't know where to begin. Thanks. BiP

Homework Statement Research the Fibonacci sequence and hence find the empirical or explicit formula for generating the nth term of the fibonacci sequence. Use this formula to show that it does indeed produce the Fibonacci numbers for n = 1 to 5. You may not use calculators, expansions of phin...

1.How to set the initial state of the Pseudo Random Sequence Generator? 2. I'm using 74LS74 D-flipflop.I'm unclear how to use clear and preset enable inputs to set the initial sequence. 3. I tried doing the experiment by directly giving the 0001 sequence through respective...

Homework Statement Is the sequence {((-1)^n)/2n} convergent? If so, what is the limit? Homework Equations The Attempt at a Solution I'm thinking that it is convergent by the alternating series test, but I am not certain. The limit part I'm not sure how to go about it. Is it...

Homework Statement Is the sequence {n} convergent? Homework Equations The Attempt at a Solution I believe that it is not convergent. I'm thinking that I could show this by a Proof by contradiction, but I am not certain. Am I going down the right route? Thanks.

State whether the sequence converges and if so, find the limit (n+1)1/2/2(n)1/2 ok so I got that it converges to 1/2, my question more so lies in the fact that why are we able to factor out a (n)1/2 from the term in the numerator? Isn't it only the denominator that we are concerned about...

Hi guys I know this limit goes to infinity lim (3^n-n) But how do I demonstrate it? Actually I know also that this type of limits goes to infinity lim \frac{a^n}{n^k},\forall a,k \in \mathbb{N},a>1 But I don't know how to prove it May you kindly help me? Many thanks

Homework Statement Suppose r>1. Prove the sequence \sqrt[n]{1 + r^{n}} converges and find its limit. Homework Equations The Attempt at a Solution It's obvious that the sequence converges to r, so I know where I need to end up. My first instinct is to use the squeeze theorem...

Given a totally finite measure μ defined on a \sigma-field X, define the (pseudo)metric d(A,B)=μ(A-B)+μ(B-A), (the symmetric difference metric), it can be shown this is a valid pseudo-metric and therefore the metric space (X',d) is well defined if equivalent classes of sets [A_\alpha] where...

Determine the monotonicity and boundedness of the sequence. 1) 4n/ (4n2 + 1)22) 2n/ 4n + 1Question: I'm having a problem in knowing whether the approach I'm using is providing the right solutions. in 1) I used the an+1/an and tried to compare their ratios. I end up with: 4n+4/ (4n2 + 8n +...

Homework Statement Prove \sum\frac{(-1)^k}{k^2} is a Cauchy sequence. Homework Equations Definition of Cauchy sequence: |a_{n} - a_{m}|<ε for all n,m>=N, n>m The Attempt at a Solution I thought if I could prove that the above summation was less than the summation of 1/k^2, the...

Homework Statement Determine whether the sequence an = 11/n2 = 21/n2 + ... + n1/n2 converges or diverges. If it converges, find the limit. 2. The attempt at a solution I have no idea what to do with this problem. I don't see why I can't simplify n/n^2 to 1/n. It was suggested to me to...

Homework Statement Let t_1=1, t_(n+1)= [1- 1/4(n^2)]*t_n for n>=1. The book says the limit is a Wallis product 2/pi, but I don't know where to start. I've been searching, but I'm lost. Could you point me in the right direction?

I've been struggling with this number sequence for some time now, and i can't find the pattern, can anyone help? the sequence is: 0, 15, 101, 8, 86, 9699, 6008, ... what comes after? any thoughts?

Homework Statement A sequence (Xn) is Cauchy if and only if, for every ε>0, there exists an open interval length ε that contains all except for finitely many terms of (Xn). Homework Equations The Cauchy Definition is: A sequence X = (xn) of real numbers is said to be a Cauchy sequence...

Homework Statement Show that the sum of a convrgent sequence and a divergent sequence must be a divergent sequence. What can you say about the sum of two divergent sequences? Homework Equations A theorem in the book states: Let {a_n} converge to a and {b_n} converge to b, then the...

NEVERMIND! IT IS 0! I SOMEHOW WAS STARING AT THE WRONG ANSWER SHEET FOR A LITTLE BIT! THANK YOU! 1. Homework Statement Determinte whether the sequence converges or diverges: (n^2)/(e^n)2. Homework Equations The book says that the solution is: e/(e-1). However, the limit of the equation...

Just an idea. which number is the next in sequence? 21, 34, 57, 61,...

Be {xn} a sequence that satisfies the condition 0 ≤ x_{m+n} ≤ x_{m} + x_{n}. Prove that lim_{n ->∞} xn/n exists. I'm kind of lost in this.

I feel like I'm missing something obvious, but anyway, in the text it states: lim as n→∞ of an+bn = ( lim as n→∞ of an ) + ( lim as n→∞ of bn ) But say an is 1/n and bn is n. Then the limit of the sum is n/n = 1, but the lim as n→∞ of bn doesn't exist and this property doesn't work...

Homework Statement f_{n} is is a sequence of functions in R, x\in [0,1] is f_{n} uniformly convergent? f = nx/1+n^{2}x^{2} Homework Equations uniform convergence \Leftrightarrow |f_{n}(x) - f(x)| < \epsilon \forall n>= n_{o} \inN The Attempt at a Solution lim f_{n} = lim...

Let <zn> be a sequence complex numbers for which Im(zn) is bounded below. Prove <e^(i*zn)> has a convergent subsequence. My question on this is what possible help could the boundedness of the Im(zn) to this proof and what theorem might be of help?

Homework Statement Show that a sequence ##f_n \to f \in C[0,1]## with the sup norm ##|| ||_\infty##, then ##f_n \to f \in C[0,1]## with the integral norm. The Attempt at a Solution given ##\epsilon > 0 \exists n_0 \in N## s.t ##||(fn-f) (x)|| < \epsilon \forall n > n_0## with ##...