Sequence Definition and 1000 Threads

I have always been curious about the distance between prime numbers. I call the sequence above the frog numbers because I don't know what else to call them. They are generated from the first n odd primes. How many consecutive integers are divisible by at least one of the set. Then add 1...

Homework Statement Determine the limit of the convergent sequence: ##a_n## =##"3/n" ^ "1/n"## http://www.wolframalpha.com/input/?i=lim+as+x+approaches+infinity++%283%2Fx%29^%281%2Fx%29Homework Equations -- [b]3. The Attempt at a Solution [/b So I tried to get this series to look like 0/0 or...

Homework Statement Could anyone please help me understand this notation? What is "it" under the variables? Is it some kind of sequence notation with 2 dimensions, or sequence notation which has the sequence member number multiplied by some other variable? What is this? Also, what could 0...

Absolutely Stunning Plot of a "Random" Sequence (Picture Included)--Need Explanation So I created 10000 waves of varying heights, 50% of the waves were 2 feet, 30% 1 foot, 15% 3 feet, 4% 4 feet, and 1% 5 feet tall. I generated 10000 "random" numbers with the statement "=Rand()" (this generates...

Homework Statement The Bank of Utopia offers an interest rate of 100% per annum with various options as to how the interest may be added. A man invests $1000 and considers the following options. Option A - Interest added annually at the end of the year. Option B - Interest of 50% credited...

1. Write out the first five terms of the sequence, determine whether the sequence converges, and if so, find its limit. {(In n)/n}+∞n = 1[b]α1 = 0 α2= 0.347 α3= 0.366 α4= 0.347 α5= 0.322I'm not sure how to continue from this point forth. How to show whether or not the limit converges.

Homework Statement A 'supa-ball' is dropped from a height of 1 metre onto a level table. It always rises to a height equal to 0.9 of the height from which it was dropped. How far does it travel in total until it stops bouncing? Homework Equations The Attempt at a Solution The...

What does it mean when one refers to, Positive Negative Zero sequence voltages/currents in relation to 3 phase power system? My blunt understanding is that in say positive sequence voltages, as we rotate around the phasor diagram in a clockwise manner we see the voltages in the...

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 am attempting to learn some measure theory and am starting with liminf and limsup of sequences of sets. I found an example that is as follows: A_n={0/n, 1/n, ... , n^2/n} and I am trying to find the limsup and liminf. Homework Equations liminf \subset limsup...

I have 3 questions concerning trying to prove open and closed sets for specific sequence spaces, they are all kind of similar and somewhat related. I thought i would put them all in one thread instead of having 3 threads. 1) Given y=(y_{n}) \in H^{∞}, N \inN and ε>0, show that the set...

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...

Homework Statement Suppose |r|<1 Find the limit of {|r|^n} by treating it as a recursive sequence defined by x_1=|r| and x_n=|r|*x_(n-1) Homework Equations This is proving a theorem in the book: If |r| < 1, then the sequence {r^n} converges to 0. The Attempt at a Solution...

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...