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.

View More On Wikipedia.org
Recent contents Top users
  1. bigchaka

    Sum of rational and irrational is irrational

    Summary:: i get a proof that sum of rational and irrational is rational which is wrong(obviously) let a be irrational and q is rational. prove that a+q is irrational. i already searched in the web for the correct proof but i can't seem to understand why my proof is false. my proof: as you...
  2. C

    Understanding the Concept of Sum in Physics: A Beginner's Guide

    please help me
  3. TheBigDig

    Sum of the Expected Values of Two Discrete Random Variables

    Apologies if this isn't the right forum for this. In my stats homework we have to prove that the expected value of aX and bY is aE[X]+bE[Y] where X and Y are random variables and a and b are constants. I have come across this proof but I'm a little rusty with summations. How is the jump from the...
  4. chocopanda

    Harmonic oscillator with ladder operators - proof using the Sum Rule

    I'm trying verify the proof of the sum rule for the one-dimensional harmonic oscillator: $$\sum_l^\infty (E_l-E_n)\ | \langle l \ |p| \ n \rangle |^2 = \frac {mh^2w^2}{2} $$ The exercise explicitly says to use laddle operators and to express $p$ with $$b=\sqrt{\frac {mw}{2 \hbar}}-\frac...
  5. R

    B Sum up Questions for Gravitational Waves & Weighing Scales

    In spite of all the problems that apparently arise from my questions or from what these questions represent (among these problems 'do not seem to agree with the underlying framework'), i would be obliged if someone can answer me the following questions, which i am hesitant to ask here as a...
  6. anemone

    MHB Can $3^{2008}+4^{2009}$ be written as a product of two positive integers?

    Show that $3^{2008}+4^{2009}$ can be written as a product of two positive integers each of which is larger than $2009^{182}$.
  7. AN630078

    Finding a and d from the Sum of an Arithmetic Series

    Question 1; Method 1 If the sum of the first four terms is 139 then S4=139 139=1/2(4)(2a+(4-1)d) 139=2(2a+3d) 139=4a+6d----- [1] The part of this question that is confusing is the "the sum of the next four terms is 115". Would this mean that S8=S4+115=139+115=254? In which case...
  8. Iliody

    A Sum over backgrounds in String Theory

    Usually, I saw that string theory (perturbative, or matrix models) are made in a fixed background. Even if you consider that the metric is quantized and etc. there is an apparent physically motivated need for making a sum over topologies (manifolds, conifolds, orbifolds, and etc), for example...
  9. R

    I Why Does the Partial Derivative of a Sum Cancel Out?

    Why the summation of the following function will be canceled out when we take the partial derivative with respect to the x_i? Notice that x_i is the sub of (i), which is the same lower limit of the summation! Can someone, please explain in details?
  10. anemone

    MHB What is the sum of these trigonometric fractions?

    Evaluate $\dfrac{1}{1-\cos \dfrac{\pi}{9}}+\dfrac{1}{1-\cos \dfrac{5\pi}{9}}+\dfrac{1}{1-\cos \dfrac{7\pi}{9}}$.
  11. LCSphysicist

    Solve this vector system containing sum and dot product equations

    Seems to me the answer is a specific vector: The second forms a plane, while the first X is just a vector. The intersection between the λX that generates the (properties of all vectors that lie in the...) plane (i am not saying X is the director vector!) How to write this in vector language?
  12. M

    I What is the Function for the Value of a Convergent Series Sum?

    ##\sum_n \frac{1}{n^c}## converges for ##c\gt 1##. Is there an expression for the value of the sum as a function of ##c##?
  13. chwala

    Solving a quadratic equation as a sum and product of its roots

    for the sum, ##\frac {1}{∝^3}##+##\frac {1}{β^3}##=##\frac {β^3+∝^3}{∝^3β^3}## =##\frac {(∝+β)[(∝+β)^2-3∝β]}{∝^3β^3}## =##\frac {-b}{a}##...
  14. CricK0es

    Minimum number of numbers to express every integer below N as a sum

    I have found code to find simply the minimum numbers needed, but I need to do it without repetition given the nature of an electric circuit. I hope that is a sufficient enough explanation of the problem. Despite being an engineering project this aspect is more mathematical.
  15. Adesh

    How to prove that ##M_i =x_i## in this upper Darboux sum problem?

    We're given a function which is defined as : $$ f:[0,1] \mapsto \mathbb R\\ f(x)= \begin{cases} x& \text{if x is rational} \\ 0 & \text{if x is irrational} \\ \end{cases} $$ Let ##M_i = sup \{f(x) : x \in [x_{i-1}, x_i]\}##. Then for a partition ##P= \{x_0, x_1 ...
  16. S

    A Hartle-Hawking sum over all possible metrics?

    Physicists Stephen W Hawking and James B Hartle 1 proposed that the universe, in its origins, had no boundary conditions both in space and time. To do that, they proposed a sum over all compact euclidean compact metrics. I have heard that they only considered these metrics in order to simplify...
  17. T

    A Is physical reality more than the sum of its parts?

    There is a paper here: https://www.mdpi.com/1099-4300/19/5/188 And a lengthy article here: https://www.quantamagazine.org/a-theory-of-reality-as-more-than-the-sum-of-its-parts-20170601/ The general argument concerns causal emergence and whether all causal agency arises directly from the micro...
  18. chwala

    Find the sum of a function given a series

    since the first term is ##g(0)= \frac {1}{3}## & last term is ##g(1)=\frac {4}{6}## it follows that the ##\sum_{0}^1 g(x)##= ##\frac {1}{3}##+##\frac {4}{6}=1## is this correct?
  19. A

    Comp Sci Recursive Double code to Calculate the sum of the square roots <= a number

    #include<stdio.h> #include<math.h> double foo(int n){ if(n==1){ return(1); } if(n!=0){ return( sqrt((n)+foo(n-1) ) ); } } int main(){ int num; printf("Enter the number: "); scanf("%d",&num); foo(num); printf(" %lf ",foo(num)); return(0); }I...
  20. F

    Sum of a series from n=1 to infinity of n^2/(2+1/n)^n

    I tried to write it as n^2/2^n (1+1/2n)^n But I am stuck there and don't know what to try next.Thanks for any help in advance!
  21. D

    Not sure if I have the correct angle and mass for this sum of forces

    Balance the forces east-west: 3.5kg*sin45º + 4.2kg*cos30º - 4.8kg*sin30º - E*cosΘ = 0 E*cosΘ = 3.712 kg balance north-south: 2.8kg + 3.5kg*cos45º - 4.2kg*sin30º - 4.8kg*cos30º + E*sinΘ = 0 E*sinΘ = 0.982 EsinΘ / EcosΘ = 0.982 / 3.712 tanΘ = 0.2645 Θ = 14.8º ◄ E = 3.712kg / cos14.8º = 3.84...
  22. karush

    MHB S8.3.7.4. The sum of two positive numbers is 16.

    3.7.4. The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares? $x+y=16\implies y=16-x$ Then $x^2+(16-x)^2=2 x^2 - 32x + 256$ So far ... Hopefully
  23. agnimusayoti

    Partial Sum and Series Value

    1. Is it because the initial formula start the series from ##n = 2##? 2. If the initial formula is used, can I find ##S##, which $$S=\lim_{n\to\infty} \frac{2}{n^2-1}=\frac{2}{\infty}=0$$? Why that answer is different if the formula is changed.
  24. karush

    MHB S8.3.7.3. whose sum is a minimum

    S8.3.7.3. Find two positive numbers whose product is 100 and whose sum is a minimum $x(100-x)=100x-x^2=100$ So far Looks like it's 10+10=20Doing all my lockdown homework here since I have no access to WiFi and a PC. and just a tablet where overkeaf does not work
  25. M

    The vector sum of the electric forces exerted on a particle

    r_{13}=r_{23}=\sqrt{(30*10^{-3})^2+(90*10^{-3})^2}=\sqrt{9*10^{-3}}\\ F^E_{13}=F^E_{23}=9E9\cdot\frac{5*10^{-9}\cdot3*10^{-9}}{9*10^{-3}}=1.5*10^{-5}\\ \theta=tan^{-1}(\frac{90*10^{-3}}{30*10^{-3}})=71.565\,degrees\\ \vec{F}^E_{13}=<F^E_{13}cos\theta, F^E_{13}sin\theta> = <4.743*10^{-6}...
  26. C

    B How can I normalize these values to sum 1?

    I have calculate a serie of view factors for a given geometry and its sum is aproximately one but not exactly. My values are: 0,1134 0,1307 0,2446 0,12393 0,115053 0,010084 0,007334 0,1071 0,0145 0,0128 0,0919 0,01675 0,00463 0,00344 The sum now is equal...
  27. bagasme

    B Derivation of Cosine and Sine Method of Vector Sum

    Hello all, In high school physics, the magnitude sum of vector addition can be found by cosine rule: $$\vec {R^2} = \vec {F^2_1} + \vec {F^2_2} + 2 \cdot \vec F_1 \cdot \vec F_2 \cdot cos ~ \alpha$$ and its angle are calculated by sine rule: $$\frac {\vec R} {sin ~ \alpha} = \frac {\vec F_1}...
  28. karush

    MHB What are the factors of -48 that result in a positive sum?

    ok I don't don't know de jure on this so ... is it just plug and play?? find factors of -48 $-1(48)=-48$ $-2(24)=-48$ $-3(16)=-48$ $-4(12)=-48$ $-6(8)=-48$ check sums for positive number $-1+48=47$ $-2+24=22$ $-3+16=13$ $-4+12=8$ $-6+8=2$it looks like c. 5
  29. I

    What is the Relationship Between Probability Amplitudes and the Sum of Terms?

    I am not sure what I can do with the equation. I realize that ## \vert c_1 \vert ^2 = \vert c_2 \vert ^2 = \frac{1}{2} ## does not mean that ## c_1 ^2 = c_2 ^2 = \frac{1}{2} ## or that ## c_1 = c_2 ##, so I don't know how to use it. I think ideally I might have something like ##P = \vert c_1...
  30. jk22

    A Should tensor sum be used in matrix mechanics?

    Suppose the Bell operator ##B=|AB(1,2)+AB(1,3)+AB(2,3)|## With ##AB\in{1,-1}## Nonlocal realism implies ##B\in{1,3}## However using usual matrix sum one eigenvalues for the result of measurement can be smaller than 1, implying nonlocal realism cannot explain the quantum result. However if...
  31. A

    Expressing an Integral as a sum of terms

    e.g Can we write it as $$f(a)+f(a+dx)+f(2a+dx)+f(3a+dx)+...f(b)=\int^b_a f(x)dx$$...(?) Although $$\int f(x)dx$$ given the area tracked by thr function with the x-axis between a and b Thanks.
  32. Monoxdifly

    MHB [ASK]Show that the sum of the fifth powers of these numbers is divisible by 5

    The sum of ten integers is 0. Show that the sum of the fifth powers of these numbers is divisible by 5. For this one I don't know what I have to do at all other than brute-forcing which may even be impossible.
  33. A

    I Is the energy of a burst of light the sum of the energy of each photon?

    In A.P. French's Special relativity the author said, The mass and length of the box are irrelevant here. He said the momentum of the radiation is ##E_{radiation}/c##. We know that the momentum of a single photon with energy ##E_{photon}## is ##p_{photon}=E_{photon}/c##. So is...
  34. Saracen Rue

    B What type of sequence is this; can you express it using a sum or product?

    Hi all; I have a very basic understanding of sequences and series and recently encountered a sequence which really has me confused: $$(\frac{1}{5}+(\frac{1}{5}+(\frac{1}{5}+(...)^2 )^2)^2)^2$$ What type of sequence would you call this? I couldn't even google it because I couldn't work out how to...
  35. Saracen Rue

    B The rule for the sum of this series?

    Consider the following series with the following pattern $$\frac {1}{1×3}+\frac {1}{5×7}+\frac {1}{9×11}...$$ How would you go about working out what the general rule for this sum is? That is in the form of ##\sum_{n=a}^{b}f(n)## Any help is greatly appreciated.
  36. S

    Finding the sum of this trigonometry series

    I got answer to (a), which is 3/4 sin thteta - sin ((3^(n+1)) theta) / (4 . 3^n) but I do not know how to use this result to prove next question. I tried to change theta into pi/2 - theta so that sin change to cos or vice versa but not working. Thanks
  37. M

    MHB Digit sum rule for the divisibility by 9

    Hey! :o Let $n\in \mathbb{N}$, $2\leq m\in \mathbb{N}$ and $a\in \mathbb{Z}$. I want to show that $a\left (m+1\right )^n \overset{(9)}{\equiv} a$. I have done the following: \begin{equation*}a\left (m+1\right )^n \overset{(9)}{\equiv} a\left (0+1\right )^n \overset{(9)}{\equiv} a\cdot 1^n...
  38. K

    I The sum of these functions equals a constant

    If I have a sum ##f(x) + g(x) = c##, with ##c## a constant, does this imply that both ##f(x)## and ##g(x)## are also constants? If I just solve this equation for ##x##, I will find some values of ##x## which satisfy the equation. However, if I require that the equation be true for all ##x##...
  39. F

    I When we can change a sum to an integral?

    In physics we often change a sum to an integral.But I am not clear when can we change a sum to an integral?When a term of sum is comparable to the sum,can we change the sum to integral?
  40. karush

    MHB 2.7.3 AP calculus Exam Riemann sum

    ok basically t is 3 hours appart except between 7 and 12 of which I didn't know if we should intemperate. other wise it is just adding up the 4 $(t)\cdot(R(t))$s.
  41. M

    Find the sum of the series Σ((3n+2)/n).... (confirmation)

    Hi, this is my try:Thanks.
  42. R

    Find an expression for a sequence involving the sum of nth powers

    Example done in class: The problem and my solution: My solution seems incorrect because if I try to plug in 0, I don't get the initial condition given in the problem. Does anyone see what I've done wrong along the way? Thanks.
  43. Q

    Find the sum of all these electric currents

    First, I got rid of amperemeters with 0 values. These are 9. 11 and 12. Amperemeter 4 will show the maximum value of electric current as it is placed directly between E and F. But how to know its value? Will it be 18 mA? I doubt because 18 mA is not said to be the maximum value. All other...
  44. wirefree

    Calculating Convolution Sum for Digital Signal Processing Class

    Please see below my attempt to perform the convolution operation on two discrete-time signals as part of my Digital Signal Processing class. I suspect my folding operation, i.e. flipping one signal about k=0, might be the cause. Ostensibly the answer of the convolution sum evaluated at n=-2...
  45. P

    Problem about the sum of the divisors of a number

    I've found that ##N_1## is 1. But it's really tiresome to find them one by one. I also tried to use the equation but couldn't. Please help me out.
  46. F

    Geometric sum using complex numbers

    Solution to the problem tells us that ##S_5 + i S_6## is the sum of the terms of a geometric sequence and thus the solutions should be : $$S_5 = \frac{\sin( (n+1) x)}{\cos^n(x) \sin(x)},\,\,\,\, S_6 = \frac{\cos^{n+1}(x) - \cos((n+1)x)}{\cos^n(x) \sin(x)} , x \notin \frac{\pi}{2} \mathbb{Z}$$...
  47. C

    A Help required to sum an infinite series in a given equation

    Hi, I have a particular equation in a paper, wherein the author specifies an infinite series. The author has apparently found the sum of the series and calculated the equation. Can anyone please help me in understanding how to sum such a series. I have attached part of the paper with the...
  48. U

    Finding the sum of a geometric series

    I'm using the sum of a geometric series formula, but I'm not sure how to find the ratio, r. The n is confusing me. The solution is below, but I'm having trouble with the penultimate step.
  49. martina1075

    Evaluate Sum - Couldn't Arrive at Answer

    Couldn’t arrive to the answer
  50. martina1075

    Evaluating a Sum: Understanding the Solution

    Cannot conclude the answer
Back
Top