Sum Definition and 1000 Threads

Homework Statement What are the possible results of the measurement of the sum of the x and z components of the spin angular momentum of a spin-1/2 particle? Sx = Spin angular momentum operator x Sz = Spin angular momentum operator x Homework Equations The Attempt at a...

Here is the question: I have posted a link there to this thread so the OP can see my work.

So the question is Evaluate (x-2)dx as the integral goes from -2 to 2 using the definition of a definite integral, choosing your sample points to be the right endpoints of the subintervals… Ok, so i understand how to do this problem if it gave me an actual number of interval like n=6 but it...

Homework Statement If you sum this from one to infinity. Ʃ (cos(1/(n)^2 - cos(1/(n+1)^2) Homework Equations The Attempt at a Solution Ʃ (cos(1/(n-1)^2 - cos(1/(n+1)^2) This is telescoping if you work that out for the partial nth partial sum you get cos(1) -...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement https://scontent-b-mia.xx.fbcdn.net/hphotos-prn2/v/1419845_10201044047645089_1286462043_n.jpg?oh=adc74f67f112c0697cbfba79b4fa81fc&oe=5283F9AB Homework Equations delta x = (b-a)/n The Attempt at a Solution Well, from the delta x formula I can figure out the...

Homework Statement https://scontent-b-mia.xx.fbcdn.net/hphotos-prn2/v/1456973_10201043975243279_1765184125_n.jpg?oh=05b39611ad70d28d837ed219e1b0f2aa&oe=52838593 Homework Equations The area can be approximated by using the sum of the areas of the rectangles. Area of rectangle = change...

Homework Statement Hello guys, I need to prove that the sum of complex roots are 0. In the Boas book, it is actually written 'show that the sum of the n nth roots of any complex number is 0.' I believe it's equivalent. The Attempt at a Solution I have managed to obtain this summation. It is...

\(\DeclareMathOperator{\Ima}{Im}\) \(\DeclareMathOperator{\Res}{Res}\) Given \[ \Ima\left[\int_{-\infty}^{\infty}\frac{e^{iz}}{z(\pi^2 - z^2)}dz\right]. \] I know the integral is equal to \[ 2\pi i\sum_{\text{UHP}}\Res(f(z); z_j) + \pi i\sum_{\mathbb{R}\text{ axis}}\Res(f(z); z_k). \] However...

Homework Statement Rewrite the given sum of iterated integrals as a single iterated integral by reversing the order of integration, and evaluate. $$\int_0^1 \int_0^x sin x dy dx + \int_1^2 \int_0^{2 - x} sin x dy dx$$ Homework Equations None The Attempt at a Solution I drew the domains of...

Hello. When I was in Mathematical Olympiad in our district, I got a example which I can not solve :-( Now, I am very interested in, how to do it. I don't know, my brother - teacher don't know, my friends don't know. I think you can solve it :-) Can you help me? It isn't my homework and I...

As far as I know there is no explicit formulas but is this true? I've tested it in Matlab with random matrices and It seems true! cond(A+B) =< cond(A) + cond(B) Where can I find a proof for this hypothesis?

Homework Statement Suppose that ∫X,Y(x,y) = λ2e-λ(x+y), 0 ≤ x, 0 ≤ y Find E(X + Y) Homework Equations E(X + Y) = E(X) + E(Y) The Attempt at a Solution Since the expected vale of a sum is the sum of the expected values, I attempted to find the marginal pdfs of the joint pdf...

Homework Statement . Let ##E## be a Banach space and let ##S,T \subset E## two closed subspaces. Prove that if dim## T< \infty##, then ##S+T## is also closed. The attempt at a solution. To prove that ##S+T## is closed I have to show that if ##x## is a limit point of ##S+T##, then ##x \in...

How to Take the sum of moments ! Homework Statement Hi i am doing static equilibrium exercises in textbook. Homework Equations But I don't know how to find sum of moments at P when its come to angle. This is a drawing The Attempt at a Solution I have No idea ! I was...

Electron is a charge, what means concrete configuration of electric field, growing to infinity in the center (if it would be a point particle). It is also a magnetic dipole moment - concrete configuration of magnetic field growing to infinity. And a mass - concrete configuration of gravitational...

I would like to calculate sum of torque on object composed of one container of helium II liquid and one container of gas with low pressure. I know you think it's 0, but I would like to be sure (I think it's not 0, but it's only my intuition). It's not a theoretical problem, so I take in account...

Hi! I want to write a program in c, that calculates the sum [1+sum{1/(i(i+1)) from 1 to n}]. I declared the variables as float. When I run the program with n=9, the output is 1.899999976, but when I calculate this with a calculator the result is 1.9. Where is the error?

Obtain the probability of getting a sum of 13, when four fair dice are rolled together once. if we do by just calculating all possible values of sum,then it will take more time. so,we can do above problem as Multinomial Coefficents of sum i.e.,x1+x2+x3+x4 = 13 where,1<= xi <= 6,for all 1<= i <=...

A set A of non-zero integers is called sum-free if for all choices of a,b\in A, a+b is not contained in A. The Challenge: Find a constant c > 0 such that for every finite set of integers B not containing 0, there is a subset A of B such that A is sum-free and |A| ≥ c|B|, where |A| means the...

I am reading the paper on the Casimir effect and they measure the space in between the plates using a sum and the energy of the vacuum without the plates using an intregal. Why do they use the sum and intregal, should they be switched.

Hi everyone, :) I encountered this question and thought about it several hours. I am writing down my answer. I would greatly appreciate if somebody could find a fault in my answer or else confirm it is correct. :) Problem: Let \(V_1,\,\cdots,\,V_k\) be subspaces in a vector space \(V\)...

How would you Integrate a Sigma Sum?

I'm doing problem section 15 chapter 1 by Boas. I don't want to ask about a particular problem in there but she often gives this kind of instruction, "By computer or tables, find the exact sum of each of the following series." My question is, what kind of table she is referring to? I take it...

In a matrix the sum of element of a matrix in a row times it's co factor of that elemt gives the determinant value, but why does the sum of element of a matrix times cofactor of different row is always zero?

Homework Statement Hey everyone! So to elaborate the title a bit more: basically I have to show that the natural representation of S_{3} is a direct sum of the one-dimensional irreducible representation and the two-dimensional irreducible representation of S_{3}. Homework Equations Im...

Hi MHB, This problem vexes me until my mind hurts. Problem: Find the sum of the first 11 terms of the series \frac{19}{99}+\frac{199}{999}+\frac{1999}{9999}+ \cdots Attempt: I managed only to find the expression of the nth term of the given series and I got...

Homework Statement Let us choose at random a point from the interval (0,1) and let the random variable X_1 be equal to the number which corresponds to that point. Then choose a point at random from the interval (0,x_1), where x_1 is the experimental value of X_1; and let the random variable...

Homework Statement Prove Ʃ1/(n^2) as n goes to infinity = (∏^2)/8 Homework Equations The Attempt at a Solution No idea how to start. Pls guide. Thanks

Suppose that x\in H, where H is a Hilbert space. Then x has an orthogonal decomposition x = \sum_{i=0}^\infty x_i. I have a linear operator P (more specifically a projection operator), and I want to write: P(x) = \sum_{i=0}^\infty P(x_i). How can I justify taking the operator inside the...

Let $p$ be the sum and $q$ be the product of all real roots of the equation $x^4-x^3-1=0$. Prove that $q<-\dfrac{11}{10}$ and $p>\dfrac{6}{11}$.

Prove the following Euler sum \sum_{k\geq 1}\left(1+\frac{1}{3}+\cdots +\frac{1}{2k-1} \right) \frac{x^{2k}}{k}=\frac{1}{4}\ln^2\left( \frac{1+x}{1-x}\right)

Homework Statement f(t) a continuously differentiable function twice over the circle T1 cr its Fourier coefficients and σn(f,t) partial sum of Fejer. a.Demonstrate that http://imageshack.us/a/img94/5992/ds35.png b. Consider k as -n≤k≤n , using cr coefficients calculate...

I know there are many proofs for this but I am having trouble proving this fact using my book's definition. My book defines first a non negative measurable function f as a function that can be written as the limit of a non decreasing sequence of non-negative simple functions. Then my book...

Write out the minimal Sum of Products(SOP) equation given the following Karnaugh Map. YZ|WX 00 01 11 10 00 d 1 1 1 01 1 1 0 0 11 0 0 d 1 10 0 0 0 0 Need someone to check my answer. My answer: yzw + \bar{y}\bar{z} + \bar{y}\bar{w}

Hi, I am trying to make progress on the following integral I = \int_0^{2\pi} \sqrt{(1+\sum_{n=1}^N \alpha_n e^{-inx})(1+\sum_{n=1}^N \alpha_n^* e^{inx})} \ dx where * denotes complex conjugate and the Fourier coefficients \alpha_n are constant complex coefficients, and unspecified...

Homework Statement Let ##T\in L(V,V)## such that ##T^{2}=1##. Show that ##V=V_{+}\oplus V_{-}## where ##V_{+}=\{v\in V:T(v)=v\}## and ##V_{-}=\{v\in V:T(v)=-v\}##.The Attempt at a Solution I was given a theorem that said that ##V## is the direct sum if and only if every vector in ##V## can be...

It's a theoretical study. I would like to understand how the sum of forces can be at 0 if I put an object (vacuum in it) in a big liquid disk (disk is fulled with liquid), the disk is big enough for agglomerate liquid (like this works with a planet, matter is agglomarate with gravity). There is...

Show that $3^{2008}+4^{2009}$ can be written as product of two positive integers each of which is larger than $2009^{182}$

Homework Statement Three yearly losses. First: Exponential Second & Third: Weibull Losses are independent. Find the 95% VaR of the min loss Homework Equations The Attempt at a Solution My first thought was: Let L be total loss, A be first Loss, B be second loss, C be third...

Homework Statement suppose that the partial sum of the series (sigma)n=1,infinity an is given by the partial sum Sn = (-2n+9)/(-6n+15). Find an expression for an when n>1 Homework Equations Sn= (-2n+9)/(6n+15 The Attempt at a Solution So I attempted to subtract S(n-1) from S(n) to get each...

I found this on the internet, but did not find the proof. Curious to me is that the the ratio and root test have the same conditions. How can i basically prove this equality? \frac{a_{n+1}}{a_{n}} = \sqrt[n]{a_{n}} Thank you!

Evaluate sum: $\displaystyle S=\sum_{k=0}^{2n}(-1)^k{2n\choose k}{4n\choose 2k}$

converge or diverge? \sum_{n=1}^{^{\infty }}a_{n} a_{1}= \frac{1}{3}, a_{n+1}= \sqrt[n]{a_{n}} Im having problems to solve this exercise, i would like to see your solutions

Simplify \frac{\sum\limits_{k=1}^{99}\sqrt{10+\sqrt{k}}}{ \sum\limits_{k=1}^{99}\sqrt{10-\sqrt{k}}}

Put $1\le n\in\mathbb Z$ Find the Sum: $S_n=\displaystyle \sum_{k=1}^n\dfrac{2k+1-n}{(k+1)^2(n-k)^2+1}$

Wolfram MathWorld states that $$ \sum_{n=1}^{\infty} \frac{1}{n^{3} \binom{2n}{n}} = \frac{ \pi \sqrt{3}}{18} \Big[ \psi_{1} \left(\frac{1}{3} \right) - \psi_{1} \left(\frac{2}{3} \right) \Big]- \frac{4}{3} \zeta(3) $$ where $\psi_{1}(x)$ is the trigamma function. But I can't get my answer in...

The Total Sum of $5$ Digit no. which can be formed with the Digit $0,0,1,1,2,2,3,3,4,4,4,5,6$ [a] without Repetition of Digit. [b] with Repetition of Digit

The Total Sum of $5$ Digit no. which can be formed with the Digit $0,1,2,3,4,5,6,7$. [a] when repetition of digit is allowed [b] when repetition of digit is not allowed

I have a sum \sum_{n=-\infty}^{\infty} f(n) which I do not want to consider the convergence of in the normal sense, but I want to talk about the limit \lim_{N\to \infty} \sum_{n=-N}^{N} f(n). I know that when this limit exists the sum is _____ convergent, or is a _____ sum, where _____ is...