Sequence Definition and 1000 Threads

Homework Statement Is the sequence {(n!)/(n^n)} convergent or divergent. If it is convergent, find its limit. Homework Equations Usually with sequences, you just take the limit and if the limit isn't infinity, it converges... That doesn't really work here. I know I'm supposed to write out the...

I have been trying to find the nth term of the following sequence: -1, 5, -17, 65... I am thinking that the nth term has (-1) ^n . It doesn't appear to be a geometric or arithmetic sequence. I am stymied.

Homework Statement Determine the convergence or divergence of the sequence with the given a_n . If it converges, find the limit. \displaystyle a_n = \frac{n^2}{(2n+1)} - \frac{n^2}{(2n-1)} The Attempt at a Solution [/B] I am not confident enough with sequence and series to know that I have...

Homework Statement Find the limit of the following sequence: Homework Equations \lim_{n \rightarrow + \infty} \sqrt[4] {2n + 1} - \sqrt[4] {n + 1} The Attempt at a Solution I've tried multiplying the first radical by ## \frac{ \sqrt[4] {2n - 1} } { \sqrt[4] {2n - 1} } ## to make the radical...

$a_1=2 ,$ and $a_{n+1}=\dfrac{a_n+4}{2a_n+3},\,\, n\in N$ find :$a_n$

Homework Statement Courant states that a convergent sequence is necessarily bounded; that is, for all n, the absolute value of term an is less than or equal to some number M. My question is does this apply to the sequence given by an = 1/(n-1)? Homework Equations As n approaches infinity, an...

Let $U_1,\,U_2,\,\cdots$ be a sequence defined by $U_1=1$ and for $n>1$, $U_{n+1}=\sqrt{U_n^2-2U_n+3}+1$. Find $U_{513}$.

Homework Statement 36, 4, 20, ... The first term of the sequence above is 36, and the second term is 4. Each term after the second is the average (arithmetic mean) of the two preceding terms. Which term of the sequence is the first that is not an integer? a. the fourth term b. the...

Homework Statement how do we get the n th term of a sequence if it is given in form of ##x_{ n+1 }=f({ x }_{ n })## and the p th term is given Homework Equations I figured we may get it if we get it in the form of ##x_{ n+1 }-{ x }_{ n }## but how?can we even get it?if yes,under...

Oddly enough, I don't remember doing a problem like. I have had a problem where I've been given the explicit formula and then asked to use induction to prove that it's correct. I think that I'm supposed to back-substitute sn into the recursion formula and go from there.

Homework Statement Find the general term of 0, 4, 22, 118, 718, 5038, 40318 if a1 = 0, a2 = 4 and so on. The Attempt at a Solution I have tried getting the differences between them, even going 4 levels deep, but that isn't working obviously, I tried seeing if the ratios are the...

$\sqrt{\text{mbh}_{29}}$ Challenge: Sn = 3, 293, 7862, 32251, 7105061, 335283445, 12826573186, ?, ?, 44164106654163 S1 through S7 begin an infinite integer sequence, not found in OEIS. 1) Find S8 and S9. 2) Does S10 belong to Sn? 3) If S10 is incorrect, what is the correct value of S10...

Hi everyone, I recently began a grad program and we have started taking a course in stochastic methods. However I can't figure out the answer to a question posed by the professor which is: http://i.imgur.com/dkdEDMo.jpg http://imgur.com/dkdEDMo He proved this by contradiction. It started...

Hello, it is known that given a certain recurrence relation that describes a sequence of numbers, it is often possible to obtain a function f[n] that directly yields the n-th number of the sequence. This is usually accomplished by using powerful techniques involving generating functions or the...

I want to prove that if the sequence a_n satisfy that a_{n+1}=a_n\left(1-c\frac{a_n}{1+a_n}\right) then a_n*c*n\rightarrow 1 for all positive c. Like when c=1, then a_n*n\rightarrow 1, but if c\neq 1, it's difficult to prove.

I kind of know what limits are, or at least believe I do: I think that a limit of a sequence is just an approximation/intuitive way to finding a number (if it exists) to which a sequence tends. For example, 1, 2, 3, 4... tends to +∞, while 1/10, 1/100, 1/1000... tends, "obviously/intuitively"...

A sequence of integers ${x_i}$ is defined as follows: $x_i=i$ for all $1<i<5$ and $x_i=(x_1x_2\cdots x_{i-1})-1$ for $i>5$. Evaluate $\displaystyle x_1x_2\cdots x_{2011}-\sum_{i=1}^{2011} (x_i)^2$.

Homework Statement The problem and solution are attached as TheProblemAndSolution.jpg. Homework Equations Definition of the limit of a sequence. The Attempt at a Solution I understand how P = ϵ + |A| can be seen as an upper bound that proves that the sequence is bounded, but for the last bit...

Homework Statement How do you determine if the limit of (1+1/n^2)^(n^2) exists and what it is? This cannot use logarithms at any point. Homework Equations (1+1/n)^n --> e The Attempt at a Solution Let N=n^2 Given (1+1/N)^N --> e, then (1+1/n^2)^(n^2) must --> e also. Is...

I'm starting sequences and series, and I have to prove that the following is increasing, nonincreasing, decreasing, or nondecreasing. $$S_n = \frac{2^n}{n!}$$ I've tried $S_{n+1}-S_n >$ or $<$ than $0$, $\frac{S_{n+1}}{S_n}$, and I don't think I've learned differentiating factorials so I...

Homework Statement I'm referring to the question and solution for part (b) in the attached TheProblemAndSolution.jpg file. Homework Equations Definition of limit. The Attempt at a Solution Should the equation with the two things in brackets have absolute value bars instead of brackets...

Homework Statement Let $$(a_n)$$ be a sequence such that $$\lim_{n\rightarrow +\infty}n(a_n)=0$$. 1) What is $$\lim_{n\rightarrow +\infty}(1 + {\frac{1}{n}} + (a_n))^n$$ 2) For which value of p and l, after some n is $$(b_n)=\frac{n^{p \ cos(n\pi)}}{(1 + l + (a_n))^n}$$ properly defined. p...

Show that 2^n/n! Converges to 0 by showing that 2^n/n! <= 4/n My problem is in showing 2^n/n! <= 4/n I know 4/n goez to 0, but how to get the inequality to be true? Doing some rough work I noticed that it "appears" to be true for n>=3. Would induction be the way to go about this step...

Hi, New to this topic, and need some help. My task is to find the convolution between $ y= x ∗ h$ where $x = u_n - u_{n-N}$ and $h_n = u_n - u_{n-M}$ and $M\ge N$ are positive integers My understanding is that in general, $ y= x ∗ h = \sum\limits_{m=-\infty}^\infty x_m h_{n-m} $ so for my...

Hi guys, I'm on the verge of sandwiching this particular sequence but I need rather tight upper estimate to trap the limit to 1. I can only manage to get the sequence that converges to ##e## as the current upper estimate. Is it possible to get tighter bound than that? \\ 1 +...

Homework Statement The last two terms, are added together to produce the next term ##-33,x,y,z,88## ##\text{Find }x,y\text{ and }z## Homework Equations ##y=x-33## ##x+y=z## ##y+z=88## The Attempt at a Solution By substituting the expression for y in the third equation for the first equation...

like these problems for example. if it converges then I am supposed to find the limit. $a_n=\frac{\sin\left({2n}\right)}{1+\sqrt{n}}$ $\left|\sin\left({2n}\right)\right| \le 1$ $a_n=\frac{(-3)^n}{n!}$ $\left|a_n\right| > 0$

Hey guys, I have a couple more questions. For the first one, taking the limit to infinity obviously equals 0 so it should be convergent, right? Also, for the second one, the limit as n approaches infinity for gives me indeterminate form, so I took the derivative which just gave me ln(n)...

only had a brief intro to algorithms like this Given an amount of money A between.01 and .99, this determines the breakdown of A into quarters (q) dimes (d) nickels (n) pennies (p) q:=A div 25 A:=A mod 25 d:= A div 10 A:= A mod 10 n:= A div 5 p:= A mod 5 I have to trace the...

A sequence is defined recursively by $a_1=2007$, $a_2=2008$, $a_3=-2009$, and for $n>3$, $a_n=a_{n-1}-a_{n-2}+a_{n-3}+n$. Find $a_{61}+a_{63}$.

Hello! This is my second post about sequence reactances. This time- its in induction motor. To my understanding ( once again ) - In any network (symmetrical or unsymmetrical) , there would be 3 components- positive sequence component, negative sequence component and zero sequence...

Hi all! I am currently learning fault study in power systems. To my understanding- In any network (symmetrical or unsymmetrical) , there would be 3 components- positive sequence component, negative sequence component and zero sequence component. Question: For generators and transformers ...

1. Write down the general term of each of the following sequences in simplest form: So far I have been using guess and check to find the solutions, but it doesn't seem much use when you get to a sequence more complicated like this: 1, -4, 7, -10, 13, ... I really need to find an equation that I...

There is a sequence which has the first 3 terms listed as $1,\,94095,\,5265679\cdots$. The 50th term has all but one digit. If the missing digit is $a$, find the $a$th term from this sequence.

Homework Statement Let ##X## be a topological space. Let ##A_1 \supseteq A_2 \supseteq A_3...## be a sequence of closed subsets of ##X##. Suppose that ##a_i \in Ai## for all ##i## and that ##a_i \rightarrow b##. Prove that ##b \in \cap A_i##. Homework Equations The Attempt at a Solution...

I am having difficulty trying to find any history in mathematics of the concept that the decimal number system is not just a product of human ingenuity. This anthropic assumption (and assumption is all that is) seems to have entirely precluded the contrary hypothesis that decimal sequence...

Homework Statement * "/" means divided by * 1/a , 1/b , 1/c are consecutive terms in an AS, where a,b,c ε R\0. (whatever that means haha) express b in terms of a and c. give your answer in its simplest form. *thats all it says* Homework Equations there are none :) The...

Homework Statement a, b and c are consecutive numbers in a geometric sequence, where a+b ≠ 0 and b+c ≠ 0 * "/" means divide * Show that 2ab/a+b, b and 2bc/b+c are consecutive terms in an arithmetic sequence The Attempt at a Solution i know this has something to do with it...

Hello everybody, this is my first post. I was wondering, what math a physicist needs. I know about the mathematical methods books, but I was hoping to learn as much math as I can rigorously. (I find it fascinating) So what kind of course sequence would encompass a lot of the math needed...

Using the fact that the Natural Nos are complete .then prove that every Cauchy sequence in Natural Nos converges in N and the converse. I do not even know if we can have a Cauchy sequence in Natural Nos. What would be the appropriate metric to use in our Cauchy sequence??

Let the sequence ${x_n}$ be defined by $x_0=2$ and $x_n=\frac{x_{n-1}}{2}+\frac{1}{x_{n-1}}$ for $n \ge 1$. Find the limit.

Homework Statement 1) If one is using light bulbs to detect phase sequence then it is wise to connect them in series with circuit resistor. Why ? 2) There is short circuit in phase "A". In which case is short circuit voltage larger, in four-drive (?) system or in three-drive (?) system ...

Homework Statement Compute \sum\frac{4}{(-3)^n}-\frac{3}{3^n} as n begins from 0 and approaches infinity Homework Equations The Attempt at a Solution I'm just getting started on sequences and series, and so far learned about the limit test, comparison test, arithmetic / geometric...

Hello, here is the problem that I have: Can you please tell me how to determine what is the sequence of the output. I can see it misses 101 and 010 and it repeats 000 and 100. I think both 101 and 010 are initial states. The answer I have for repeated sequence is 011, 111, 110, 100...

Question 1 write the first 4 terms in the sequence defined by a 1 = -2, a n+1 = an/n! this what I tried a2 = -2/1 a3 = -2/2 a4 = -1/6 Question 2 determine the following sequences converges or diverges 1- an = sqrt(n^2 -3 )/ 5th rt(n^2) what I would try is to divide both...

Let $a_1 = 1$, $a_2 = a_3 = 2$, $a_4 = a_5 = a_6 = 3$, $a_7 = a_8 = a_9 = a_{10} = 4$, and so on. That is, $a_n ∶ 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, . . . . $ What is $a_{2013}$?

Let the sequence {$a_n$} be defined by $a_1 = 1$ and $a_n = \frac{1}{1+a_{n-1}}$ for $n \ge 2$ . Find the limit.

Assume the sequence of positive numbers ${a_n}$ converges to L. Prove that $\lim_{n \to \infty} \sqrt[n]{a_1a_2...a_n} = L$ (The nth root of the product of the first n terms) Since ${a_n}$ converges we know that for every $\epsilon> 0$ there is an $N$ such that for all $n > N$ $ |a_n -...

determine whetehr the sequence diverges or converges, if converges find its limit $$\displaystyle a_n = (1 + \frac{2}{n})^n$$ my teacher is trying to tell me this converges to e^2 ... HOW?

If ##\left\{ a_{n} \right\}## is monotone increasing and there exists ##M \in \Re## such that for every ##n \in N## ##a_{n} ≤ M## prove that ##\left\{ a_{n} \right\}## converges. (Hint: Use the Cauchy sequence property. Recall: 1) ##\left\{ a_{n} \right\}## is Cauchy if and only if...