What is Sum: Definition and 1000 Discussions

Sum, sumu, sumon, and somon (Plural: sumd) are the lowest level of administrative division used in China, Mongolia, and Russia. The word sumu is a direct translation of a Manchu word niru, meaning ‘arrow’ Countries such as China and Mongolia, have employed the sumu administrative processes in order to fulfil their nations economic, social and political goals. This system was acted in the 1980s after the Chinese Communist Party gained power in conjunction with their growing internal and external problems. The decentralisation of government included restructuring of organisational methods, reduction of roles in rural government and creation of sumu’s.

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  1. A

    How to deal with this sum complex analysis?

    Homework Statement Homework Equations Down The Attempt at a Solution As you see in the solution, I am confused as to why the sum of residues is required. My question is the sum: $$(4)\cdot\sum_{n=1}^{\infty} \frac{\coth(\pi n)}{n^3}$$ Question #1: -Why is the beginning n=1 the residue...
  2. C

    Expressing kinetic energy as sum of vector and tensor terms

    Homework Statement A system of N particles described by the vector coordinates ##\mathbf{r}_k, k = 1,2, \dots, N ## subject to 3N - f constraints can be expressed in terms of generalised coordinates ##q_i, i=1,2, \dots, f## by ##\mathbf{r}_k = \mathbf{r}_k(q_1, q_2, \dots, q_f, t)## a) Prove...
  3. 22990atinesh

    How to find sum of the given infinte series

    Homework Statement The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is Homework EquationsThe Attempt at a Solution No Clue
  4. K

    (Tribology) Can someone explain Contact Curvature Sum to me?

    I am having a hard time grasping contact curvature sums. Can someone give me a link to where there is a guide or a youtube video? or can someone help me here please. Here are the equations: 1/Rx = 1/rax + 1/rbx 1/Ry = 1/ray + 1/rby 1/R = 1/Rx + 1/Ry The question is this: The ball-outer...
  5. A

    The sum of angles in 3D is not 90 while in 2D it is?

    Sorry for the confusing tittle but I could not explain it better. Here is what I am trying to ask: When you have 2 axis(x and y) such as the image below, the sum of the two angles, a and b will always be equal to 90 degrees. a + b = 90degrees However when you add a 3rd axis(x, y and z, making...
  6. J

    Are \bigoplus and \times interchangeable in direct sum and direct product?

    Under what conditions are the symbols \bigoplus and \times intechangangable?
  7. Randall

    I finding the sum of this series

    Homework Statement Find the sum of the series from k=0 to infinity of ((4^k)-(3^k))/(5^k) Homework Equations I'm not sure exactly. I know the test for divergence is if lim n approaches infinity of the function from m=1 to infinity does not equal 0 then the series cannot diverge The Attempt...
  8. R

    Finding Value of Sum of Geometric Series

    Homework Statement Let ## S_k , k = 1,2,3,…,100 ## denote the sum of the infinite geometric series whose first term is ## \frac{k-1}{k!} ## and the common ratio is ##\frac {1}{k}##. Then value of ##\frac {100^2}{100!} + \sum\limits_{k=1}^{100} | (k^2 - 3k + 1)S_k | ## is Homework Equations...
  9. G

    Is the Sum of Deviations from the Median Always the Smallest?

    Dear Friends! Is sum of deviations from median always minimum,in comparison to deviations from mean,mode or any other observation?Why?
  10. R

    Sum of last two digits of 27^27

    It's an amazing question to find sum of last two digits of 27^27 by not using that wolframalpha or calculators.I think binomial theorem would be of help here but not able to apply.can anyone tell me the answer by any method?
  11. anemone

    MHB How can factorization prove the compositeness of a given expression?

    Prove that for every positive integer $a$, the integer $5^{4a}+5^{3a}+5^{2a}+5^a+1$ is composite.
  12. N

    Are waves always the sum of sine waves?

    I saw that somewhere and it is supposed to be something Fourier came up with but I can't find somewhere why... Please explain (with mathematical description if possible)
  13. A

    Mean of a sum of random variables

    Homework Statement If Y=X1+X2+...+XN prove that <Y>=<X1>+<X2>+...+<XN> Homework Equations <Y>=∫YP(Y)dY over all Y. The Attempt at a Solution I only seem to be able to show this if the Xi are independent, and I also think my proof may be very wrong. I basically have said that we can write the...
  14. N

    Fermi distribution: Sum over states --> integral over states

    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...
  15. J

    What is the sum of this infinite series?

    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!
  16. M

    MHB Direct sum of free abelian groups

    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...
  17. Math Amateur

    MHB Sum of Submodules - infinite family case

    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...
  18. andyrk

    Computing a Series Sum: n2 + (r-1)2 to n2 + (n-1)2

    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)
  19. anemone

    MHB Find the sum of the real roots

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

    Expectation value of a SUM using Dirac notation

    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...
  21. D

    If a sum is 0, is the summand 0?

    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?
  22. RJLiberator

    Can Variable Coefficients Be Used in Geometric Series Sums?

    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...
  23. A

    Sum of ordinates mean value of functions

    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...
  24. Albert1

    MHB Sum of Sequence $(a_{n+1}+3)(2-a_n)=6$ to 100

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

    Finding potential U from sum of forces F

    < Mentor Note -- Thread moved to Homework Help from technical Physics forum > 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 calculations...
  26. Math Amateur

    MHB Sum of an Indexed Family of Submodules - Northcott, pages 8-9

    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...
  27. V

    Double rotation, friction and sum of energy

    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...
  28. D

    MATLAB Sum Y Values for Repeating X Values to Plot 0-Crossing Point

    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...
  29. A

    MHB Finding an Integral for a given Riemann Sum

    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...
  30. A

    MHB Evaluating infinite sum for e^(-x) using integrals

    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...
  31. A

    Trying to find the infinite sum of e^-x using integration

    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...
  32. RJLiberator

    Find the Sum of this Alternating Series

    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...
  33. D

    Conservation of mechanical energy vs sum of forces

    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...
  34. B

    MHB Sum of k-powers and divisibility

    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.
  35. D

    Sinc function as a sum of cosines

    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
  36. T

    Why do only even values of n show up in the expansion of sin4x?

    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...
  37. N

    MHB MGF relating to random sum of random variables

    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) =...
  38. P

    Sum somewhat similar to Basel problem?

    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...
  39. C

    Can we sum out the vacuum state ##|0\rangle\langle 0|## ?

    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...
  40. DataGG

    Perturbation theory, second-order correction - When does the sum stop?

    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...
  41. 9

    Statistics: given total sum of squares, find R²

    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]...
  42. evinda

    MHB Prove that the sum is equal to -1.

    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...
  43. K

    Vector Sum of Forces Experiment

    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...
  44. G

    Finding Min Value of Sum of Cosine Angles in 3D Space

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

    Compute ∫√(25 - x^2) dx from 0 to 5 using an infinite Riemann Sum

    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 +...
  46. D

    Sum of a vector parallel and orthogonal to.

    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...
  47. Albert1

    MHB Calculate Square of Sum ∑1..9999

    \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
  48. stevendaryl

    Infinite Sum of Powers: Is There a Closed Form for the Series?

    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
  49. diegzumillo

    Normal matrix as sum of self adjoint and commuting matrices

    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...
  50. L

    Statistics Sum of Squares x*y Proof

    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...
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