Sum Definition and 1000 Threads

Homework Statement http://web.phys.ntnu.no/~kolausen/TFY4230/.oldExams/17_eksdes12.en.pdf solution: http://web.phys.ntnu.no/~kolausen/TFY4230/.oldExams/18_losdes12.en.pdf Look at problem 4a, formula (27) or the expression between (29) and (30). My professor keeps converting sums into...

Sum= ...- 1 + 1 -1 +1-1+1... until infinite It is just an infinite sum of -1 plus 1. Can anyone tell me the sum of this infinite series and a demonstration of that result? THanks!

Show the direct sum of a family of free abelian groups is a free abelian group. My first thought was to just say that since each group is free abelian we know it has a non empty basis. Then we can take the direct sum of the basis to be the basis of the direct sum of a family of free abelian...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 1.4 which introduces modules. I need help with one of the definitions included in the statement of Proposition 1.4.4. Proposition 1.4.4 reads as follows: In (2) in the above Proposition Bland...

Can someone explain how to compute the sum of the following series? 1/(n2 + (r-1)2) + 1/(n2 + (r)2) + 1/(n2 + (r+1)2) + ...1/(n2 + (n-1)2)

Find the sum of the real roots for $2x^8-9x^7+20x^6-33x^5+46x^4-66x^3+80x^2-72x+32=0$.

Homework Statement Consider a one-dimensional particle subject to the Hamiltonian H with wavefunction \Psi(r,t) =\sum_{n=1}^{2} a_{n}\Psi _{n}(x)e^{\frac{-iE_{n}t}{\hbar}} where H\Psi _{n}(x)=E_{n}\Psi _{n}(x) and where a_{1} = a_{2} = \frac{1}{\sqrt{2}}. Calculate the expectation value of the...

Hey guys, Was just wondering something. Suppose I have an equation of the form \sum_{i=0}^{n}\frac{1}{x_{i}}(a-by_{i})=0, how would I solve this? do I just set the summand = 0?

Homework Statement I am giving the sum: k=1 to infinity Σ(n(-1)^n)/(2^(n+1)Homework Equations first term/(1-r) = sum for a geometric series The Attempt at a Solution [/B] With some manipulation of the denominator 2^(n+1) = 2*2^n I get the common ratio to be (-1/2)^n while the coefficient is...

I am having trouble deciphering the opening gambit of an explanation of mean values of functions. It begins as follows: "Consider the part of the curve y = f(x) for values of x in the range a ≤ x ≤ b." A graph is shown with a curve cutting the x-axis at c with a shaded positive area bounded...

given :$(a_{n+1}+3)(2-a_n)=6$ $(a_n\neq 0, a_1=1)$ please find :$\sum_{n=1}^{100} \dfrac {1}{a_n}$

< Mentor Note -- Thread moved to Homework Help from technical Physics forum >[/color] Hi, I had an exam and I had this question: A force acts on a particle of mass m, and its components are: Fx = 2axy + by2 + 6cz Fy = ax2 + 2byx Fz = 6cx a) Does this force is conservative? Show your...

I am reading D. G. Northcott's book, Lessons on Rings, Modules and Multiplicities. On pages 8 and 9, Northcott defines/describes the sum of an indexed family of submodules, as follows:https://www.physicsforums.com/attachments/3507 At the conclusion of the above text on the construction of the...

Hi, I posted my question on another forum: http://physics.stackexchange.com/questions/143377/one-disk-ring-in-double-rotation-and-sum-of-energy but it is "on hold" and nobody knows where is the error, so I try to post here if you are agree ? I can understand if you close the question...

Hello guys, Have an issue here. I have a large array of numbers, X and Y values.These are coordinates of 9 curves on the same x-axis , so the X values are repeating (433 X values repeating 9 times), what I need to do is to sum Y values for each X value separately. and then plot it (bar plot...

Hello, This question is purely inspired by: http://mathhelpboards.com/calculus-10/evaluating-infinite-sum-e-x-using-integrals-12838.html My other question. Anyhow, How do you find the integral for a given specific Riemann sum. Suppose the same one given in the link; $= \displaystyle...

Hello, I have began my journey on infinite sums, which are very interesting. Here is the issue: I am trying to understand this: $\displaystyle \sum_{n=1}^{\infty} e^{-n}$ using integrals, what I have though: $= \displaystyle \lim_{m\to\infty} \sum_{n=1}^{m} e^{-n}$ $= \displaystyle...

Hello, I am well aware of the ratio method, and the sum = 1/(1-r) but I want to try this method. I am trying to understand this: \displaystyle \sum_{n=1}^{\infty} e^{-n} using integrals, what I have though: = \displaystyle \lim_{m\to\infty} \sum_{n=1}^{m} e^{-n} = \displaystyle...

Homework Statement Find the sum of starts at 0 to infinity ∑ (cos(k*pi))/pi^k First, I determined that it does, indeed, converge with the alternating series test. Second, I found the answer to be pi/(1+pi) via wolfram alpha. But I am at a loss on how to find the answer here. This is a...

When do one use the principle of conservation of mechanical energy to find the velocity of a mass, and when would you use the sum of forces equals to the mass times acceleration, and there after use a ds=v dv in order to find the velocity. The specific question related to this is a spring fixed...

Let $a_{1},\dots,a_{n},\, n>2$ positive and distinct integer. Prove that the set of primes divisors of the numbers $$a_{1}^{k}+\dots+a_{n}^{k}$$with $k\in\mathbb{N}$ is infinite.

Hello, If you plot y=sin(x)/x and also plot y = summation of 0.01*cos(n*x/100) over n = 0 to n =100 you essentially get the same graph. Is there any formal proof that relates the sinc function to a sum of cosines. Thanks

Homework Statement Hello, I found this problem in the book I borrowed from the library, but this book does not have solutions in the back...I tried to lent the solution book but the library does not have it...so could someone help me out? The question is: It is possible to decompose the...

Hi all I am doing this question right now and I don't even know how to start it up. I know that it's in relation to a sum of a random number of random variables, but I don't know how to continue on from that. I've read my textbook and it states some definition for an MGF which is: $M_{y}(t) =...

Homework Statement For a problem in quantum, I am finding the probability of a particle initially in the ground state on a circular loop of length L being in the nth state of the string after it is cut (becomes an infinite square well, and we assume the wavefunction is not disturbed during this...

For example, when we write down the operator definition of quark fragmentation matrix element: ##\Phi_{ij} = \sum_X \int d^4 x e^{ikx}\langle 0|\psi_i(x)|P,X\rangle\langle P,X|\bar{\psi}_j(0)|0\rangle##. Can we rewrite is as: ##\Phi_{ij} = \sum_X \int d^4 x e^{ikx}\langle...

I've no idea if I should be posting this here or in the general forums. This is not really an exercise as much as an example. I'm not understanding something though: 1. Homework Statement Using perturbation theory, find the exact expression for the energy given by the hamiltonian...

Homework Statement Given: Σ(xi - x̄)² = 500 Σ(yi - ybar)² = 800 (total sum of squares, SST)) Σ(ŷ - ybar)² = 400 (total sum of estimators, SSE) Σ(xi - x̄)²(yi) = 200 Σ(xi - x̄)²(εi) = 0 n = 1000 s² = 4 Find (or explain why you cannot find): β1 β0 variance of β R² Homework Equations [/B]...

Hello! (Smile) I want to prove that at the field $\mathbb{Q}_p$, where $p$ is a prime, it stands: $$-1=\sum_{0}^{\infty} (p-1)p^i$$ That's what I have tried so far:$$-1=\sum_{i=0}^{\infty}(p-1)p^i =(p-1)+(p-1)p+(p-1)p^2+\dots \\ \Rightarrow 1-1=1+p-1+p^2-p+p^2-p^2+\dots \\ \Rightarrow...

Homework Statement http://cgscomwww.catlin.edu/sauerb/AP12/AP12_Labs/AP12_Lab_4_Forces_files/image002.jpg My experiment is like this picture found in the net. The weight in the middle is called R in my experiment, while the left one is P and the right Q. Now there is one question asked, the...

Dear Friends! How can I find the minimum value of sum of cosine of angles between three unit vectors in three dimension space

Homework Statement Integrate √(25 - x^2) dx from 0 to 5 using an infinite Riemann Sum Homework Equations lim n→∞ Σ_(i=1)^n i = n(n+1)/2 lim n→∞ Σ_(i=1)^n i^2 = n(n+1)(2n+1)/6 The Attempt at a Solution Δx = (b - a)/n Δx = (5 - 0)/n Δx = 5/n f(x_i) = √(25 - [a + iΔx]^2) f(x_i) = √(25 - [0 +...

Homework Statement v = 3i - j u = 2i + j - 3k Express vector u as a sum of a vector parallel to v and a vector orthogonal to v.Homework Equations Proj of u onto v = [ (u • v) / |v|^2 ]v Expressing vector u as sum of a vector parappel to v and a vector vector orthogonal to v >> u = [Proj of...

$$\left(\sum_{n=1}^{9999}\frac{\sqrt{100+\sqrt{n}}}{\sqrt{100-\sqrt{n}}}+\sum_{n=1}^{9999}\frac{\sqrt{100-\sqrt{n}}}{\sqrt{100+\sqrt{n}}}\right)^2$$

This isn't quite a calculus question, but it didn't seem right for any of the other mathematics forums, either. Does anybody if there is a closed form for the following infinite series: \sum_n x^{n^2} for 0 < x < 1

Homework Statement I need to show that any normal matrix can be expressed as the sum of two commuting self adjoint matrices Homework Equations Normal matrix A: [A,A^\dagger]=0 Self Adjoint matrix: B=B^\dagger The Attempt at a Solution A is a normal matrix. I assume I can write...

Homework Statement Prove that \sum[(x_{i} - \overline{x})(y_{i} - \overline{y})] = \sum[(x_{i} - \overline{x})y_{i}] Homework Equations None. The Attempt at a Solution I tried using the fact that the sum of the mean values is just the mean value, because the sum of a constant...

I have an experiment in which I want to extract the distribution function of a process. I expect it to be Gaussian. Each data point measured is an entire distribution, f(x), but I am forced to average over many points such that the result of the experiment is the sum of many measurements of...

Homework Statement Let ##X_k## be iid uniform discrete on ##\{0,...,9\}##. Find the distribution of ##\sum\limits_{k=1}^{\infty} \frac{X_k}{10^k}##Homework Equations The Attempt at a Solution I've tried a lot of things, I've tried decomposing ##X_k## into 10 bernoulli trials, I've tried using...

How does the spin of a pair of particles work if both particles are known to be chiral? generically if I sum the spins of two different (EDIT: spin 1/2, indeed ;-) particles I expect to get a triplet with S=1 \uparrow\uparrow, \uparrow\downarrow+\downarrow\uparrow, \downarrow\downarrow and...

the problem: In how many ways can we write the number 4 as the sum of 5 non-negative integers?I realize this is a generalized combinations problem. I can plug it in using a formula, but I want to understand the logic behind why the generalizaed combination formula works. More specifically, my...

Can someone guide me with the steps to differentiate a geometric sum, x? ^{n}_{i=0}\sumx^{i}=\frac{1-x^{n+i}}{1-x} If I'm not wrong, the summation means: = x^0 + x^1 + x^2 + x^3 + ... + n^i Problem is: I have basic knowledge on differentiating a normal numbers but how do I apply...

Homework Statement V(t) = [2t - 4] u(t) u(4 - t) I need to express this a sum of step and ramp functions. Homework Equations The Attempt at a Solution I have absolutely no idea how to proceed

I ran into this problem, and would like to see if there is something more elegant. Suppose we have a sequence $a_1, a_2, \dotsc, a_n, \dotsc$ where $a_k$ is the (running) sum of rolling a standard 6-side die $k$ times. E.g. What's the chance of saying the number $2$ appears in this sequence...

Equate the limit $$\lim_{n \to \infty} \frac1{n} \sum_{i = 1}^n \sum_{j = 1}^n \frac1{i + j}$$ Note : This was a challenge from a user in mathstackexchange. From a glance, there should be many ways to do it, so partly I posed this problem to see how the resident analysts in MHB handle it...

Find a positive number such that the sum of the number and its reciprocal is as small as possible. Full marks for proving your answer is correct. Process: let $a>0$ $$f(a)=a+\frac{1}{a}$$ $$f'(a)=1-\frac{1}{a^2}=\frac{(a+1)(a-1)}{a^2}$$ The critical numbers are $0$, $\pm 1$, but only $1$ is...

Find the sum of all real numbers $a$ such that $5a^4-10a^3+10a^2-5a-11=0$.

Hiya. I got to an interesting bit in a calculus book, but as usual I'm stumped by a (probably simple) algebraic step. The author goes from: (ds)^2=(dx)^2+(dy)^2 to: ds=\sqrt{1+\left(\frac{dy}{dx}\right)^2}dx I understand moving the square root across, but I don't understand how the...

Hi. Assume there's a probability ##q## for a guy to take a step to the right, and ##p=1-q## to take one to the left. Then the probability to take ##n## steps to the right out of ##N## trials is ##P(n) = {{N}\choose{n} }q^n p^{N-n}##. Now, what is ##<n>##? My textbook in statistical physics...

Find an integer $k$ for which $\dfrac{1}{k}+\dfrac{1}{k+1}+\dfrac{1}{k+2}+\cdots+\dfrac{1}{k^2}>2000$.