Sequence Definition and 1000 Threads

Hi all, suppose I have a random discrete sequence like x= [1 2 3 2 5 2 4 2 3 1 6 3 5] (where possible outcomes are 1,2,3,4,5 or 6) and wanted to get its frequency distribution vector f=[2 4 3 1 2 1] which means frequency of occurrence of 1 is 2 times, 2 occurs 4 times , and so on. I...

Homework Statement A sequence (xj) where j can go from 0 to infinity satisfies the following: (1) x1= 1 and (2) for all m≥n≥0, xm+n+ xm-n= (1/2)(x2m+x2n) Find a formula for xj and prove that the formula is correct Homework Equations The Attempt at a Solution All I have done so...

Suppose for each given natural number n I have a convergent sequence (y_i^{(n)}) (in a Banach space) which has a limit I'll call y_n and suppose the sequence (y_n) converges to y. Can I construct a sequence using elements (so not the limits themselves) of the sequences (y_i^{(n)}) which...

Homework Statement For the state table shown below, show the output sequence when the input sequence is as given below. Assume the machine starts in state A. x : 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 z : x>0...1 A A,1 B,0 B A,0 C,1 C D,1 A,0 D A,0 B,1 Homework Equations N/A The...

Homework Statement \sum_{n=1}^{\infty} \frac{n^{k-1}}{n^k+c}, where k is a positive integer.Homework Equations The Attempt at a Solution I found that it was discontinuous at x = (-c)^{1/k}; and to determine if the sequence is decreasing, I took the derivative which is--I think--f'(x) =...

A real sequence $\{x_n\}$ satisfies $7x_{n + 1} = x_n^3 + 6$ for $n\geq 1$. If $x_1 = \frac{1}{2}$, prove that the sequence increases and find its limit. To be increasing, we must have $s_n\leq s_{n + 1}$. What next? My Analysis game is weak.

Homework Statement suppose that (s_n) and (t_n) are sequences in which abs(s_n)≤t_n for all n and let lim(t_n)=0. Prove that lim (s_n)=0. The Attempt at a Solution I find absolute values to be really sketchy to work with I'm really in the dark if this is at all correct: Let ε>0 be given, then...

Homework Statement Show that \delta_n(x) = ne^{-nx} \quad \mathrm{for}\quad x>0 \qquad = 0 \quad \mathrm{for}\quad x<0 satisfies \lim_{n\longrightarrow\infty}\int_{-\infty}^\infty \delta_n(x)f(x)\mathrm{d}x = f(0) The attempt at a solution The hint says to replace the upper limit...

I'm trying to write a program in fortran that will create a sequence of numbers (starting with a number that I input) that follow the following constraints: If the number (n) in the sequence is even, then the next number in the sequence will be n/2. If the number (n) in the sequence is odd, then...

1. The problem is if an is convergent then prove or disprove by giving a counter example that an2 is also convergent. 2. Since an is convergent then for all ε>0 there exists n0\in N such that lan-Ll<ε for all n>=n0 So I then tried squaring (an-L) which gives an2 -2anL +L2<ε2 How do I...

[b]1. Homework Statement [/b I want to see if a sequence converges by deciding on monotonicity and boundness. The sequence is: an=(n+1)/(2n+1) How to I go about determining if it converges or not based on those two factors? I am lost on how to go about it. THanks for any help...

Homework Statement The sequence is a_n = \frac{n^P}{e^n} Homework Equations The Attempt at a Solution If I did L'Hopital's rule P times, would the final product look like: P!\times lim_{n \rightarrow \infty} = \frac{1}{e^n} ?

Hi all, I have a general question along with a specific one. Could anyone give me an intuitive explanation of finding limits of convergent sequences? I have a test and just do not understand how to consistently find the answer to these problems. I can understand intuitively obvious ones, but...

What is the general term for the sequence 8,12,18,27,... First of all I know that i can make a polynomial or whatever function pass through these points but I make a relation I just want to build the general term of it I took the difference between any two terms I choose 40 8 , 12 , 18 ...

Homework Statement I have to prove that the sequence a(n)=(n^3-n +1)/(2n+4) diverges to infinity. Homework Equations The Attempt at a Solution Observe that n^3-n +1 > (1/2)n^3 and 2n+4≤4n in n≥2 I am now stuck on how to proceed. I am confused on opposite inequalities for...

Homework Statement I attached the problem and solution as one file. Homework Equations The Attempt at a Solution I just can't quite follow the solution. Could someone perhaps explain what the author is doing?

Homework Statement a_n = \frac{(2n -1)!}{(2n)^n} Homework Equations The Attempt at a Solution I am not exactly sure how to solve this problem.

Homework Statement 3, -3/2, 3/4, -3/8,... Homework Equations The Attempt at a Solution I began to write, (-1)^{n+1} \frac{3}{...}, but I began to despair once I came upon the denominator. I know that every term's, except 3, denominator can be written as a power of two, but I...

Use a geometric or algebraic argument to find a formula for the partial sums $A_n$ of an arithmetic sequence. I know that the partial sum is $S_n = n/2(2a_1+(n-1)d)$ where d is the difference. $A_n = \sum\limits_{k = 1}^n a_k$ I can come up with $n/2(a_1+a_n)$ but how do I get the difference?

Z-transform of a conjugated sequence ("a straightforward" exercise) Homework Statement The conjugation property is expressed as x^*[n] \stackrel{Z}{\leftrightarrow} X^*(z^*) This property follows in a straightforward maner from the definition of the z-transform, the details of which are left...

Homework Statement 14 Ʃ 2(4/3)^n n=1 Homework Equations Sn=a(1-r^n)/(1-r) The Attempt at a Solution 2(1-[4^14]/[3^14])/(-1/3)=330.74 However, the answer sheet gives ~441 as the answer, and I confirmed it by doing it by hand. Why is the equation not working? What's wrong?

Construct a sequence of interpolating values \(y_n\) to \(f(1 +\sqrt{10})\), where \(f(x)= \frac{1}{1+x^2 }\) for \(−5≤x≤5\), as follows: For each \(n = 1,2,…,10\), let \(h =\frac{10}{n}\) and \(y_n= P_n (1+\sqrt{10})\), where \(P_n(x)\) is the interpolating polynomial for \(f(x)\) at nodes...

Homework Statement Prove that the sequence {a_n} converges to A if and only if lim n--->∞ (a_n-A)=0. Homework Equations The Attempt at a Solution It's an if and only if proof, but I'm not sure how to prove it. Please help!

Homework Statement Prove that if E \subset X and if p is a limit point of E, then there is a sequence \{p_{n}\} in E such that p=\lim_{n\to\infty}\{p_{n}\} (I presume that there is an invisible "p_{n} \rightarrow p implies that" at the beginning of the sentence). Homework Equations -...

Homework Statement Show that if sn\leqb for all but finitely many n, then lim sn\leqb. Homework Equations The Attempt at a Solution My question is regarding the absolute value portion of the proof: by contradiction: Call lim sn s. Suppose s>b. Then l sn-s l <...

Hi all, I am really confused about the random variables Toss a coin three times, so the set of possible outcomes is Ω={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Define the random variables X = Total number of heads, Y = Total number of tails In symbol, X(HHH)=3...

When a foreign protein is introduced in a rabbit or a mouse, its immune system attacks the protein by antibodies which specifically recognize the protein. How does the body know the sequence of the protein such that it manufactes an antibody which will specifically target that non-self protein.

Hello, It is my understanding that if we have a sequence defined as follows:an+1=(ψ)an + (λ)Then if ψ≥1 or ψ≤-1, the sequence diverges. If -1<ψ<1, the sequence converges to: λ/(1-ψ)I was working problems in a book and one of the problems said that the following sequence converges...

Homework Statement The question is attached in the picture. The Attempt at a Solution Since V0 = 1, Thus V1 = \stackrel{1}{2}∏R2 which is a constant. Then shouldn't Vn be as in the picture?

please guide me on how to discover the formula for this sequence --> 1,2,1,2,3,4,1,2,3,4,5,6,1,2,3,4,5,6,7,8,... responses are highly appreciated.

Thomas-Finney defines a bounded sequence as follows: - A sequence an is said to be bounded if there exists a real number M such that |an| ≤ M for all n belonging to natural numbers. This is equivalent to saying -M ≤ an ≤ M So, if all terms of a sequence lies between, say -1 and 1, i.e...

Homework Statement A sequence \{s_n\} is defined by s_{n+1} = \frac{1}{2} (s_n + s_{n-1}); s_1 > s_2 > 0 I have to prove that the sequence is convergent and I have to find the limit. Homework Equations The Attempt at a Solution I tried equating the limit of both sides to get s =...

Homework Statement A>0, B can be any number Homework Equations To show that lim(n->∞) (1/n)log[A((1+sqrt(5))/2)^n +B((1-sqrt(5))/2)^n] = (1+sqrt(5))/2The Attempt at a Solution I used Lhopital's Rule to solve this and got log((1+sqrt(5))/2) So, I don't know what is wrong. If you guys...

Homework Statement Please see the attached photo. (The one with the green highlighter), I haven't written it out to avoid mistakes. Homework Equations None. The Attempt at a Solution I have constructed a moore state diagram, a state transition table and come up with boolean...

Hello everyone! I was wondering whether the sequence (-1)^n is converging or diverging. According to Wikipedia, a sequence that doesn't have a limit (i.e, which doesn't converge), is automatically divergent. (-1)^n doesn't have a limit, yet all its values oscillate between 1 and -1, and...

Please help! I'm stuck on modeling the function for the # of toothpicks in the nth figure. Thank you so much. Renee

Homework Statement Is the sequence xn=[(n5+7n+3)7]/[(7-n4)6] bounded? ] The Attempt at a Solution I've managed to tell that the sequence is not bound because as n tends to ∞ xn also tends to ∞ but it took me a relatively long time. Is there any way of telling this by just...

I was just googling around and I came across this problem. Let (X,d) be a metric space. Let (An)n \in N be a sequence of closed subsets of X with the property An \supseteq An+1 for all n \in N. Suppose it exists an m \in N such that Am is compact. Prove that \bigcapn\in NAn is not empty...

In the definition, 1) why must you find a n_0 \in N such that \forall N \geq n_0? You might as well say find a n_0 \in R such that \forall N > n_0. Just a matter of simplicity? 2) Why must |x_n - a| < \epsilon hold? I think |x_n - a| \leq \epsilon is fine as well, given that it must hold...

Hello, all, I am an adult college student and I'm having a terrible time "understanding" a particular astronomy question. I do not ask that any of you answer the question, but I am asking that maybe some of you can re-structure the original question so that I may have a clue as to what's...

Given three characters that have a specific probability assigned to each of them: Ω: .2 θ: .3 β: .4 What is the probability of having, say a sequence of 6 of these characters where the first and last character is a θ?

Homework Statement Consider the finite length x[n]= 2δ[n]+δ[n-1]+δ[n-3] We perform the following operation on this sequence: (i) We compute the 5-point DFT X[k] (ii) We compute a 5-point inverse DFT of Y[k]=X[k]2 a) Determine the sequence y[n] for n= 0, 1, 2, 3, 4 b) If N-point...

Hello, I'm wondering if there are any tricks to quickly determine the parity of the weight of a binary number, i.e., whether it's even or odd. I'm not interested at all in the actual weight of the number, but in the parity of it. I know that if say x = a XOR b, then x has odd weight iff...

I've been curious about the Fibonacci sequence for quite a while now, so I decided to study it on my own. I noticed that you can get the sequence by adding the numbers on the pascal triangle diagonally, or by simply adding the number that precedes the next (0,1,1,2,3,5,8...). I then watched a...

Homework Statement xn+1 = xn + cosxn , n>=1 where x0 E [π/4 , 3π/4] = D. Show it converges, find rate of convergence.Homework Equations contraction theoremThe Attempt at a Solution Setting a function f(x) = x+cosx we have f'(x) = 1 - sinx, f''(x)= -cosx. Now f' >= 0, so f is increasing. For...

Conjecture Regarding Rotation of a Set by a Sequence of Angles. Consider the following sequence, where the elements are rational numbers mulriplied by \pi: (\alpha_{i}) = \hspace{2 mm}\pi/4,\hspace{2 mm} 3\pi/8,\hspace{2 mm} \pi/4,\hspace{2 mm} 3\pi/16,\hspace{2 mm} \pi/4,\hspace{2 mm}...

Hi. I`m working on some exercises but I could`t find any clue for this one: Find a bounded sequence (as like the norm) in l^2 Hilbert space,that weakly converges to 0 (as like the weak topology) but doesn`t have any convergent subsequences (as in strong topology). Could someone help me?

how do i determine the formula for the sequence below? 1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,...,n,n,n,n,n,...,n,... need some instructions. thanks in advance

Hii everyone, I have a sequence {ai,1<= i <=k} where i know the sum of this sequence(say x). I want to know the sum of another sequence {bi, 1<=i <=k}(at least a tight upper bound) where bi=ai*(1/2^i). Or in other words, if you know the sum of the ratio sequence and sum of 1 sequence, how to...

Hi guys, I'm new here at this forum, but I don't understand this problem. Let a1 be a positive real number. Define a sequence an recursively by a(n+1) = (an)^2 - 1. Show that an does not converge to zero. (Is there a1 such that the sequence an converges to some non-zero value?) I'm...