Sequence Definition and 1000 Threads

Homework Statement This problem is taken directly out of a textbook. "The first three terms of a geometric sequence are 1,2, and 4. Susanna said the 8th term of this sequence is 128. Paul said the 8th term is 29. Explain how the students found their answers. Why could these both be...

The sequence a_1,\;a_2,\;a_3,\cdots is defined by a_1=1, a_{2n}=a_n, a_{2n+1}=a_{2n}+1. Find the largest value in a_1,\;a_2,\;a_3,\cdots,\; a_{1989} and the number of times it occurs.

Here is the question: Here is a link to the question: Determine whether the sequence is divergent or convergent? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

HI, does anyone know a decent site where I can find a few product identities? I googled it, but all that came up were trig identities. I am not looking for those; I am specifically looking for product of a sequence identities: ∏

I am looking for a different proof that ##(S_n) = \frac{1}{n}## is cauchy. The regular proof goes like this (concisely): ##\left|\frac{1}{n} - \frac{1}{m} \right| \leqslant \left|\frac{m}{nm}\right| \ (etc...) \ <\epsilon ## but I was thinking about an alternative proof. Is my proof...

Homework Statement This is taken from STEP I 1990, Q4. (i) The sequence a1, a2, ..., an, ... forms an arithmetic progression. Establish a formula, involving n, a1, and a2, for the sum of the first n terms. (ii) A sequence b1, b2, ..., bn, ... is called a double arithmetic progression if the...

Homework Statement There are patterns made up of square tiles which I can not draw but only describe... Pattern 1 has 1 grey tile in centre and 8 dotted tiles around it Pattern 2 has 4 grey tiles in centre and 12 dotted tiles aound it Pattern 3 has 9 grey tiles in centre and 16 dotted...

Homework Statement Consider the sequence n1, n2, n3, ... that satisfies the recurrence relation nk = nk-1 / k + 1 for all integers k ≥ 2 with the initial condition that n1 = 1. Find the explicit formula nk for the nth term of the sequence? 2. The attempt at a solution I calculated...

Hello, How to create a batch file that shuts down system at a particular time (not countdown but when the time approaches, it shuts down the system) after closing all the open programs? I don't want to use task scheduler P.S. how to make it a batch file that runs even when the system is...

Hello. I have a problem. I don't know how to finish my proof. Maybe someone of you will be able to help me. So task is: Suppose that fn and gn are function of the sequence. fn simply convergence(? don't know if english term is same) to f, and gn simply convergence to g. Need to prove that...

If ##p## is a limit point of ##E## then ##\exists \ (p_n) \ s.t. (p_n) \rightarrow p## For the sequence construction, can I just define ##(p_n)## as such: ##For \ q \in E, \ \ define \ (p_n) := \left\{\Large{\frac{d(p,q)}{n}} \right\}_{n=1}^\infty##

Homework Statement I am trying to solve this problem and need help with one aspect.Homework Equations sequence: 0,-1,0,1 -- repeated.The Attempt at a Solution How do I make every 4th term of the sequence a negative number? for instance i have: (1 + (-1)^n)/2 but i don't know how to...

Homework Statement lim x-> infinity 3n+2/5n

(Typewriter sequence) Consider the following sequence of functions on [0,1]. Let f1= X[0, 1\2], f2= X[1\2, 1], f3= X[0, 1\4], f4= X[1/4, 1\2], f5= X[1\2, 3/4], f6= X[3/4, 1], f7= X[0, 1\8], etc. Where X is the Characteristic function. (a) Prove that fn does not converge for any x in [0,1]...

SOLVED Prove that the functional sequence has no uniformly convergent subsequence -check n \in \mathbb{R}, \ \ f_n \ : \ \mathbb{R} \rightarrow \mathbb{R}, \ \ f_n(x) =\cos nx We want to prove that {f_n} has no uniformly convergent subsequence. This is my attempt at proving that: Suppose...

Hi. Could help me with the following problem? Let f be a real function, increasing on [0,1]. Does there exists a sequence of functions, continuous on [0,1], convergent pointwise to f? If so, how to prove it? I would really appreciate any help. Thank you.

(definite integral problem) write as an expression Homework Statement \int0k 3x2 suggest an expression for definite integrals from x=0 to x=k Homework Equations see below The Attempt at a Solution when k= 0, \int0k 3x2 = 0 when k= 1, \int0k 3x2 = 1 when k= 2, \int0k 3x2 = 8...

Homework Statement Converge or diverge?Homework Equations \displaystyle a_{n} = \frac{(-1)^{n+1}}{2n-1}The Attempt at a Solution all i know is to perhaps take ln of numerator and denominator to get the exponent down below?

I have a vague understanding of how to derive the sine function from a Maclaurin Sequence however this isn't helping me figure out why: (1 - \frac{x^{2}}{4π^{2}}) (1 - \frac{x^{2}}{9π^{2}}) (1 - \frac{x^{2}}{16π^{2}})... = \frac{π^{2}}{x(x+π)}\frac{sin x - sin π}{x - π} Any help would be...

Homework Statement Show the following sequence to diverge, or converge. Determine if monotonic. a sub n=n+(1/n) The Attempt at a Solution I understand that the sequence does diverge. I found this because the limit as n→∞ the limit is going to ∞ as well. I found that the sequence is monotonic...

The general definition for the limit p of a sequence (pn) is \forall \epsilon > 0, \exists N \in \mathbb{N}:n \in \mathbb{N} \geq N \implies d(p_n,p) < \epsilon So, for the experience, I want to derive the limit of the sequence (1/n)_{n \in \mathbb{N}}. I would like detailed and harsh...

Homework Statement Prove that the sequence a_n=\frac{1}{n}+\frac{(-1)^n}{n^2} converges to 0 using the definition of convergence. The Attempt at a Solution I'm pretty stumped on this one...all I've written is |\frac{1}{n}+\frac{(-1)^n}{n^2}-0| < \epsilon The only way I know how to...

The increasing sequence 1, 3, 4, 9, 10, 12, 13 ... consists of all those positive integers which are powers of 3 or sum of distinct powers of 3. Find the 100th term of this sequence.

Homework Statement how to prove that the sequences space lp is subspace of lq for p smaller than q? Homework Equations The Attempt at a Solution I try to imply holder inequality but meanwile unsuccesfully

Homework Statement Let {a_n} be a sequence | (a_n+1)^2 < (a_n)^2, 0 < (a_n+1) + (a_n). Show that the sequence is convergent Homework Equations n/a The Attempt at a Solution So I am feeling like monotone convergence theorem is the way to go there. It seems to me that (a_n+1)^2 <...

Homework Statement I need to explain DSSS in my applied mathematics project (duration is three minutes of my talk). How do two users agree on which channel and the time to listen to so that they can exchange messages? Homework Equations Use Barker sequence as a channel encoder and...

I have a problem that asks for the subsequential limits, the limit superior, and the limit inferior for the sequence s_n = 4 ^{\frac {1} {n}} I haven't had trouble with my other problems, but I don't see any subsequences in the sequence (other than the sequence itself). Am I missing somthing?

Is my understanding of the concept of ##\underset{n}{Sup} \ S_n## correct? for instance, given the sequence: ##{S_n} = sin(\frac{n \pi}{2}). \frac{n+2}{2 n}## Then ##\underset{1}{Sup} \ S_n \ = \ \frac{3}{2}## ##\underset{10}{Sup} \ S_n \ = 0## ##\underset{k≥n}{Sup} \ S_n...

Homework Statement Homework Equations The Attempt at a Solution above picture ! Exam in 3 hours :( please help

Hi there, I recently discovered a formula for the nth term that works for any finite sequence of numbers. I was just wondering whether a formula has already been discovered, and if not, how and where I should publish it. To give you an example of what i mean: one formula for the nth...

Here is the question: Here is a link to the question: Real Analysis Sequences 10pts? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

A function f has a root of multiplicity $m>1$ at the point $ x_*$ if $f(x_*)=f'(x_*)=...=f^{(m-1)}(x_*)=0$. Assume that the iteration$ x_{k+1}=x_k-mf(x_k)/f'(x_k)$ converges to $x_*$. If$ f^{(m)}(x_*)≠0$, prove that this sequence converges quadratically.(We may use the Taylor's series, but I...

Homework Statement This isn't quite homework (though it's close), but I'm working on a quantum circuit and wish to implement an iterative method to find the square root of a number using elementary arithmetic operations (and without reciprocals). I've gotten most of it down, but the error...

Homework Statement Need to prove that the following sequence is monotonic ( decreasing ). \frac{1}{n^2}+\frac{(-1)^{n}}{3^n}Homework Equations - The Attempt at a Solution I have idea how to prove that the sequence is decreasing that is: a_{n+1} - a_{n} ≤ 0 but in this case, I can't get the...

Has anyone here done this before? If so, kit recommendations and protocol? Any help would be awesome. Thanks!

Hi, I'm new here and, as will become obvious from my question, neither a phycisist nor a mathematician. This is not a homework question, so I post it in this forum and hope that's okay. (I've aready asked on stack exchange but as far as I can see the answers given to me there were describing a...

Here is the question: Here is a link to the question: Geometric sequence question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Let S_{1}=1 and S_{n+1}=\sqrt{2+S_n} Show that \left\{S_n\right\} converges and find its limit. Hint: First assume that the limit exists, then what is the possible value of the limit? Second, show that the sequence is increasing and bounded. Finally, follow the...

Homework Statement Find the limit of this sequence An = \frac{n^{n}}{(n+3)^{n+1}} Homework EquationsThe Attempt at a Solution The answer is 0 but my answer is 1 thank you

Homework Statement find the limit of this sequence 1) An = \frac{\sqrt{n} sin (n! e^{n})}{n+1} 2) An = 4n^{3} sin\frac{1}{n^{3}} Homework Equations The Attempt at a Solution (1) |sin n! e^n)| ≤1 |An| ≤ \frac{ \sqrt{n} }{n+1} |An| ≤ \frac{ \sqrt{n}/n...

Homework Statement Show that the sequence an= sqrt(n) is unbounded Homework Equations there is no relevant equation require. The Attempt at a Solution Actually, I'm a newbie for real analysis, I try to prove it by using contradiction method, but I stuck at half way, can anyone...

Homework Statement Find the sum of 5^1-5^2+5^3-5^4+...-5^{98} a. (5/4)(1-5^99) b. (1/6)(1-5^99) c. (6/5)(1+5^98) d. (1-5^100) e. (5/6)(1-5^98) Homework Equations The Attempt at a Solution I feel as though this is actually a simple problem and that I'm not looking at it the right way. [5^1...

Homework Statement Let Ʃ 1\(n^2-1) from n=2 to k. It says find a closed for it and prove it using sum notation. Homework Equations The Attempt at a Solution I can easily prove it by induction but I don't know what a closed form means. I tried looking it up online but there really...

I am currently looking at a number sequence to solve a puzzle. I have identified the following with the sequence: 1. There are 3,684 digits in the series (3,684 being a Keith Number) 2. The sequence 789 appears 47 times in the overall sequence (47 is also a Keith Number) I'm thinking this...

Homework Statement Say we have an infinite sequence of natural numbers A such that no K subsequences can be found adjacent such that the average of the elements in any subsequence is equal for all K subsequences. Sorry about my poor description, an example would be that {2, 3, 4, 1} wouldn't...

I quote an unsolved problem posted on December 9th, 2012 in another forum Suppose \displaystyle\lim_{n \to \infty}a_n=a, \displaystyle\lim_{n \to \infty}b_n=b and without loss of generality that the sequences are (a_n)_{n\geq 0} and (b_n)_{n\geq 0}. We have to prove $L=\displaystyle\lim_{n\to...

Homework Statement A sequence of 3-digit numbers divisible by 7 is given. Find: a) first three and last three numbers. b) how many numbers are there in that sequence. c) sum of all the numbers in the sequence. Homework Equations The Attempt at a Solution Cause they are 3...

Homework Statement The problem: Let r satisfy r2= r + 1. Show that the sequence an = Arn, where A is constant, satisfies the Fibonacci sequence an = an-1 + an-2 for n > 2. Homework Equations The given equations above are the only relevant equations. The Attempt at a Solution I...

Could anyone help me out with the monoticity of this sequence please? \frac{2\ln(n)}{\sqrt{n+1}} . It should decline. I am investigating the convergence of one series and I need it to do the Leibniz test.

Let's assume we have a coin. When it is tossed, in first 2 times it comes head, and the next time tails. It goes like that in sequence, let's say two times. 2 head, 1 tails, 2 head 1 tails.. Btw, the coin is not fake, so head and tails both have equal probability of %50. Is there a function...