Sum Definition and 1000 Threads

Homework Statement The sum of two vectors, A→ + B→, is perpendicular to their difference, A→ - B→. How do the vectors magnitude compare? The Attempt at a Solution SQRT[(A+B)^2 + (A-B)^2]

Prove that $\tan \left( \dfrac{3 \pi}{11} \right)+ 4\sin \left( \dfrac{2 \pi}{11} \right)=\sqrt{11}$. I know this problem may be stale as it has been posted countless times at other math forums, but I've seen one brilliant method to attack this problem recently, and I'm so eager to share it...

$x_0,x_1,-----,x_{2004} \in Z , \, x_0=0, \mid x_n \mid =\mid x_{n-1}+1\mid $ $for, \,\, 1 \leq n \leq 2004$ (1) $find :\,\, min\mid x_1+x_2+x_3+ ------+x_{2004}\mid $ (2) get a set of numbers $ x_1,x_2,-----x_{2004} $ satisfying your answer

Hi MHB, I have solved the problem as stated below but I don't know if it's an unique solution and even if it is, I have no idea how to prove that would be the case. Can anyone show me how to approach the problem correctly? For the equation $x^5-12x^4+ax^3+bx^2+cx-64=0$, all of its roots are...

I was trying to design some GUI for a tool I'm making and I noticed there's a hidden math problem somewhere in there. Not being one to let the opportunity slide, I decided it's worth exploring. Basically there's 3 buttons that add to a variable. What are the best values to put on those...

Hi lovely people, I recently came across a video http://www.youtube.com/watch?v=w-I6XTVZXww that said if you add all of the natural numbers from 1 to infinity, the answer is... What do you think it is? Infinity or something like that? They said it was -1/12. I watched the proof but I don't...

Hi. I need to sort out some concepts and terminology. I was wondering if there are algorithms and terminology surrounding the following situation. Lets say I want to buy some object for an amount of money, but the object cost less than the amount of money I have. I will have a remainder of...

Homework Statement Sum the series 1 + 2a + 3a2 + ... to n terms This series consists of an a.p. (with general term n) and gp general term a^(n-1) right? So the series general term is na^(n-1) So is the sum the sum of each progression times each other? i.e (1-a^n)/(1-a) *...

Homework Statement ΔABC has AB= 8 in, BC= 10in , CA= 6in . AD is the perpendicular from A to BC. DE the perpendicular from D to AB, EF the perpendicular from E to BD and so on. Show that CA + AD + DE+... is a geometric series and find it's sum to infinity. Homework Equations The...

Compute $\sqrt{2000(2007)(2008)(2015)+784}$ without the help of calculator.

Determine the sum $$\sum_{k=1}^n \dfrac{4k}{4k^4+1}$$.

If the distribution of a sum of N iid random variables tends to the normal distribution as n tends to infinity, shouldn't the MGF of all random variables raised to the Nth power tend to the MGF of the normal distribution? I tried to do this with the sum of bernouli variables and...

Evaluate the sum $\displaystyle \sum_{i=0}^n \tan^{-1} \dfrac{1}{i^2+i+1}$.

Given $p+q+r+s=0$ $pqrs=1$ $p^3+q^3+r^3+s^3=1983$ Evaluate $\dfrac{1}{p}+\dfrac{1}{q}+\dfrac{1}{r}+\dfrac{1}{s}$.

So my textbook asks to show \int^{3}_{1} x^{2}dx = \frac{26}{3}. They let the partition P = {x_{0},...,x_{n}}, and define the upper Riemann sum as U(P) = \sum^{i=1}_{n} x_{i}Δx_{i} and lower sum as L(P) = \sum^{i=1}_{n} x_{i-1}Δx_{i} I understand this part, but the next part is where I'm...

Dear everyone. First of all Merry Xmas, when everybody gets to that. I have a problem solving for a factor within a sum. My formula looks as follows: T = Æ© It * A0t The sum runs from t=1 to N, and the aim is to solve for A0, but all my calculations end up extremely messy...

If $\dfrac{\cos \alpha}{\cos \beta}+\dfrac{\sin \alpha}{\sin \beta}=-1$, evaluate $\dfrac{\cos^3 \beta}{\cos \alpha}+\dfrac{\sin^3 \beta}{\sin \alpha}$.

Is it necessary for a unit sum composed of unit fractions to include 1/2? Doing maple runs this seems to be the case, but it is not evident to me how this could be Edit: In fact it seems it could not be, given the Erdos Graham problem Erd?s?Graham problem - Wikipedia, the free encyclopedia But...

Hello I have N couples of real numbers higher than 1. Let's call them like (a0,b0), (a1,b1),...,(aN,bN) I have a number R <= N. I need the sum of all the possible products of N elements, chosing one from each couple but exactly R times the "b" element and N-R times the "a" element...

Hi, http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter7.pdf (see page 8, sum of two independent random variables). I don't understand why they had to go further into the limits, 1 < z < 2. Why do they have to do that? And also, where did they get it...

Evaluate the sum $$ \sum_{i=2}^{99}((i + 1)^2 - i^2))$$ So I found the pattern and got $$ ((3^2) - 2^2)) + ((4)^2 - (3)^2)) + ((5^2) - (4)^2)$$ ... etc etc $$100^2 -2^2 = 9,996?$$ Is this correct? #2 Evaluate the sum $$ \sum_{i=2}^{100}(i^2 -(i - 2)^2) $$ and got: $$100^2 + 99^2 - 1 =...

Homework Statement problem in in the picture Homework Equations I can't understand some parts of the equation. The Attempt at a Solution

Assume that $$\sum_{n=1}^{\infty} a^2_{n}$$ converge, and assume that $$a_{n}$$ is non-negative for all $$\textit{n} \in N.$$ Determine whether the following statement is true (and prove it) or false (and give counterexample). $$\sum_{n=2}^{\infty} \frac{a_{n}}{n^{2/3}}<\infty$$ Does anyone...

Homework Statement a_n is a sequence of positive numbers. Prove that \prod_{n=1}^{\infty} (1+a_n) converges if and only if \sum_{n=1}^{\infty} a_n converges. Homework Equations The Attempt at a Solution I first tried writing out a partial product: \prod_{n=1}^{N} (1+a_n) =...

Evaluate $h\left( \dfrac{1}{401} \right)+h\left( \dfrac{2}{401} \right)+\cdots+h\left( \dfrac{400}{401} \right)$ if $h(x)=\dfrac{9^x}{9^x+3}$.

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

Hello I have a set of sets of real numbers greater than 1. Each set can have a different quantity of numbers. Set A1 {a11, a12,...a1m1} Set A2 {a21, a22, ..., a2m2} ... Set AN {aN1, aN2, ..., aNmN} If I want the sum of all possible products that have one element from each set, that's...

Determine the sum of real roots of the equation $q^4-7q^3+14q^2-14q+4=0$.

When you have combinations where digits are 0,1,2...,m, meaning we have n=m+1 and k, is there a way to see how much of them sum up to a given number? For the sake of simplicity I have the digits 0,1,2...,7 (so n=8), and k=3. I need to find how much of these combinations WITH repetition sum up to...

Homework Statement Find the displacement using a midpoint Reimann sum with 4 subintervals of equal width. minute 0, 12, 24, 36, 48, 60, 72, 84, 96 ft/min -4, -4, 1, 4, 5, -6, 0, 5, 2 Homework Equations Displacement is the final position minus starting position. The Attempt at...

Homework Statement I'm having trouble writing a sum for this: https://scontent-b-mia.xx.fbcdn.net/hphotos-frc3/v/1420232_10201136345792485_382911431_n.jpg?oh=ebd9432103184956c863370121e326ce&oe=529332ED Homework Equations delta x = (b-a)/n n = 4 b-a = 2 delta x = 1/2 The...

Homework Statement Approximate the value of the integral of 6/(1+2x) with respect to x from 0 to 2. Use 4 subintervals of equal width and use the left endpoints. Homework Equations delta x = (b-a)/N The Attempt at a Solution The integral is the sum of 6/(1+i) from i = 0 to i = N-1 or 3...

Homework Statement Express the integral of (sinx + 1) dx over the interval [0,pi] with a Reimann Sum using 4 subintervals of equal width and letting x_i^* be the left endpoint of the subinterval [x_(i-1), x_i] Homework Equations Δx = [b-a] / n The Attempt at a Solution Δx = pi/4...

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...