Sum Definition and 1000 Threads

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. A

    What is the sum of infinite number of zeros?

    dear all, let's consider a length L and divide it into N number of small segments uniformly. Then the length of every segment should be L/N. then we add these segments up, which is L=\sum\frac{L}{N} then we take the limit N→\infty at both sides, this means...
  2. M

    Simple problems regarding sum of IID random variables

    Hi! I'm taking my first course in statistics and am hoping to get some intuition for this set of problems... Suppose I have a bowl of marbles that each weighs m_{marble}=0.01 kg. For each marble I swallow, there is a chance p=0.53 that it adds m_{marble} to my weight, and chance 1-p that...
  3. Joffan

    Sum of arbitrary vertex to midpoint vectors

    I was looking at a homework question posted here requiring proof that the vectors from the vertices of a triangle to the midpoint of the opposite edge sum to zero, and it struck me that there is a more general property: Consider a set of points, \{A_0, A_1, \ldots A_n\}. The midpoint of...
  4. N

    Alternative deduction of sum of sine and cosine

    Hi! Many students know that A\sin(x) + B\cos(x) =\sqrt{A^2+B^2} \sin{(x+\arctan \frac{B}{A})}. I have seen just one deduction of that relation, showed by set up a system of two equations, solving for amplitude and phase shift. Is it possible to deduce the relation in a vectorial way, or in...
  5. R

    Expand an equation - sum and product

    Homework Statement I have been sitting here for the last hour trying to figure it out but I can't seem to be able to find what I'm doing wrong. I need to expand an equation. Homework Equations a2 - a - 3 The Attempt at a Solution a2 - 1a - 3 The product is -3 and the sum -1...
  6. AwesomeTrains

    Partial sum of the harmonic series

    Homework Statement I have to find a natural number N that satisfies this equation: \sum^{N}_{i=1} \frac{1}{i} > 100 Homework Equations I tried finding a close form of the sum but couldn't find anything useful. The Attempt at a Solution Well after trying some numbers in maple I...
  7. anemone

    MHB Find the sum of 5a, 25b, 125c and 625d

    Given $a,\,b,\,c,\,d$ are real numbers such that $a+b+c+d=5$ $2a+4b+8c+16d=7$ $3a+9b+27c+81d=11$ $4a+16b+64c+256d=1$ Evaluate $5a+25b+125c+625d$.
  8. anemone

    MHB Find the sum of all positive integers a

    Find the sum of all positive integers $a$ such that $\sqrt{\sqrt{(a+500)^2-250000}-a}$ is an integer.
  9. G

    Integrating for approximation of a sum

    Homework Statement Find an N so that ##∑^{\infty}_{n=1}\frac{log(n)}{n^2}## is between ##∑^{N}_{n=1}\frac{log (n)}{n^2}## and ##∑^{N}_{n=1}\frac{log(n)}{n^2}+0.005.## Homework Equations Definite integration The Attempt at a Solution I began by taking a definite integral...
  10. anemone

    MHB Evaluating the Sum of $\frac{1}{k_n}$ for $n=1,2,\cdots,1980$

    Let $k_n$ denote the integer closest to $\sqrt{n}$. Evaluate the sum $\dfrac{1}{k_1}+\dfrac{1}{k_2}+\cdots+\dfrac{1}{k_{1980}}$.
  11. G

    Calculating the sum of a sequence

    Homework Statement Compute \sum\frac{4}{(-3)^n}-\frac{3}{3^n} as n begins from 0 and approaches infinity Homework Equations The Attempt at a Solution I'm just getting started on sequences and series, and so far learned about the limit test, comparison test, arithmetic / geometric...
  12. Q

    What Is the Sum of Bond Angles in a Maximized Repulsion Tetrahedron?

    Homework Statement Prove that if bonding-pair repulsions were maximized in CH3X, then the sum of the bond angles would be 450°. Homework Equations In a perfect tetrahedral molecule (e.g. methane), the sum of the bond angles is about 438 degrees (109.5° times 4). The Attempt at a...
  13. U

    Use fourier series to find sum of infinite series

    Homework Statement Find the value of An and given that f(x) = 1 for 0 < x < L/2, find the sum of the infinite series. Homework Equations The Attempt at a Solution The basis is chosen to be ##c_n = \sqrt{\frac{2}{L}}cos (\frac{n\pi }{L}x)## for cosine, and ##s_n = \sqrt{\frac{2}{L}}sin...
  14. Saitama

    MHB Infinite Sum of Powers of x over 1-x^2

    Problem: If $0<x<1$ and $$A_n=\frac{x}{1-x^2}+\frac{x^2}{1-x^4}+\cdots +\frac{x^{2^n}}{1-x^{2^{n+1}}}$$ then find $\displaystyle \lim_{n\rightarrow \infty}A_n$. Attempt: I tried to see if it can be converted to a telescoping series but I had no luck. Then, I tried this: $$\lim_{n\rightarrow...
  15. Saitama

    MHB Evaluating a sum involving binomial coefficients

    Problem: Evaluate $$\mathop{\sum \sum}_{0\leq i<j\leq n} (-1)^{i-j+1}{n\choose i}{n\choose j}$$ Attempt: I wrote the sum as: $$\sum_{j=1}^{n} \sum_{i=0}^{j-1} (-1)^{i-j+1}{n\choose i}{n\choose j}$$ I am not sure how to proceed from here. I tried writing down a few terms but that doesn't seem...
  16. M

    Understanding the Formula for the Sum of a Geometric Series

    For the question, shouldn't the sum be a(1/1-r) since we know lrl < 1 then that rn → 0 as n → ∞? I just don't quite understand why they wrote the sum is a(r/1-r). Is there a specific reason they did this? This is just a regular geometric series right? Is there any difference since the sum starts...
  17. L

    Find the sum of the first n terms

    Homework Statement Find the sum of the first n terms of the sequence U1, U2, U3... Ur Homework Equations The Attempt at a Solution $$ \sum_{r = 1}^n (1 + (-1)^r) = n + (-1)^n $$ But I don't this is right... any help?
  18. L

    What is the formula for finding the sum to n terms in a geometric series?

    Homework Statement Wn = 2 + 3(1/2)^n Homework Equations The Attempt at a Solution I am confused, all I tried so far is writing out the first 5 terms, but all that was helping me to do is basically find the Sum to infinity... so what should I do to find the Sum to n terms? I know...
  19. E

    Max of Sum of Sines: Find the Max Value for Even n

    Hi! Consider the function \frac{d^n}{dx^n} \sum_{k=1}^m \sin{kx}, \quad 0 \leq x \leq \pi/2 . If n is odd this function attains its largest value, \sum_{k=1}^m k^n at x=0 . But what about if n is even? Where does the maximum occur and what value does it take? Any help is much...
  20. Math Amateur

    Homology of Connected Sum of Two Projective Planes, P^2 # P^2

    I am reading James Munkres' book, Elements of Algebraic Topology. Theorem 6.5 on page 39 concerns the homology groups of the connected sum of two projected planes. Munkres demonstrates the following: H_1 ( P^2 \# P^2 ) \simeq \mathbb{Z} \oplus \mathbb{Z} / 2 ... ... ... (1) and H_2 ( P^2...
  21. Math Amateur

    MHB Help with 'connected sum" symbol #

    I just completed a post in the Topology and Advanced Geometry forum regarding the connected sum of two projective planes. I wanted to use the symbol # for the connected sum as is usual in the topology books I am studying - but just typing in the symbol 'upsets' latex and so my post cannot be...
  22. MarkFL

    MHB Inductive Proof: Sum of Cubes of First n Natural Numbers

    Here is the question: I have posted a link there to this question so the OP can view my work.
  23. T

    Sum of a Power Series: Finding the Sum of a Series with a Variable

    Homework Statement find the sum of the following series: \sum_{n=1}^\infty nx^{n-1} , |x|<1 Homework Equations \frac{a}{1-r} The Attempt at a Solution i know that a function representation for that series is -\frac{1}{(1-x)^2} but how is it possible to find the sum of a series with a...
  24. F

    Engineering Doubt about BCD Sum circuit using full adders

    Homework Statement I understand this BCD sum circuit. The only thing that I'm not understanding is why last full adder carry out also triggers an 6-sum in the other part of the circuit. I mean, if the nibble is not an valid BCD number, we sum six to the number. Not valid BCD numbers are...
  25. R

    Algebra, how to separate a term in the sum of two roots

    My mind has gone blank and I've suddenly forgotten basic algebra, please could someone give me direction on how to make P the subject of this equation? E = (P^2 C^2 + M^2 C^4)^1/2 + (P^2 C^2)^1/2 thanks for any help
  26. anemone

    MHB What is the sum of all positive solutions?

    Find the sum of the positive solutions to $5+x\lfloor x \rfloor-2x^2=0$.
  27. anemone

    MHB Evaluating an Infinite Sum of Binomial Coefficients

    Evaluate $\displaystyle\lower0.5ex{\mathop{\large \sum}_{n=2009}^{\infty}} \dfrac{1}{n \choose 2009}$.
  28. Seydlitz

    Showing that V is a direct sum of two subspaces

    Hi guys, I have this general question. If we are asked to show that the direct sum of ##U+W=V##where ##U## and ##W## are subspaces of ##V=\mathbb{R}^{n}##, would it be possible for us to do so by showing that the generators of the ##U## and ##W## span ##V##? Afterwards we show that their...
  29. jk22

    Sum of the probabilities equals 3 in bipartite covariance ?

    If we consider a bipartite system as in EPRB experiment we get the probabilities : p(++)=p(--)=1/4*(1-cos(theta)) p(+-)=p(-+)=1/4*(1+cos(theta)) p(+A)=p(+B)=p(-A)=p(-B)=1/2 Thus the sum of all the probabilities equals 3... How does that come ? Is it because in fact there are only...
  30. N

    Why is 1+2+3+4+5+... equal to -1/12?

    I'm not sure which category this post actually belongs to, or if the title of this post is even accurate. I guessed Calculus was the closest one. I watched this video on the web after a professor told me this mathematical phenomenon (http://www.youtube.com/watch?v=w-I6XTVZXww‎). It asserts...
  31. A

    Converting Between K-Space Sum and Integral for Macroscopic Solids"

    How is it exactly i convert between a k-space sum an integral? Assume that we have some macroscopic solid. Periodic boundary conditions leads to kx,ky,kz = 2π/L, so each k-space state fills a volume (2π/L)3 or has a density of V/(2π)3. To then count for instance the number of state with...
  32. J

    Sum and product of coefficient binomials

    Given two coefficient binomials \binom{a}{b} and \binom{c}{d} is possbile to express the sum and product those coefficient binomials as one other?
  33. L

    MHB Sum of distances the same as the former

    find a point on the axis OX whose sum of distances to landmarks: (2, 0) and (0, 3) is minimal. Answer (2,0) As the title says it is the same as the former So the equations must be sqrt((x-2)2+02)+sqrt((x-0)2+ 9) because the point is (x.0) but it seems I am wrong because i don't get the answer
  34. T

    What is the distribution of the sum of two random vectors?

    I am trying to derive the distribution for the sum of two random vectors, such that: \begin{align} X &= L_1 \cos \Theta_1 + L_2 \cos \Theta_2 \\ Y &= L_1 \sin \Theta_1 + L_2 \sin \Theta_2 \end{align} With: \begin{align} L_1 &\sim \mathcal{U}(0,m_1) \\ L_2 &\sim...
  35. K

    Sum and differences identities equations

    Homework Statement Which is equivalent to: cos(∏/2 + x) - cos(∏/2 - x)? A) -2cos(x) B) -2 C) 0 D)-2sin(x) Homework Equations Cos (A-B) The Attempt at a Solution I am totally stuck :( please help!
  36. alyafey22

    MHB Proving the Double Sum of Exponentials Equals ae^a-e^a+1

    Prove the following \sum_{n=1}^\infty \sum_{m=1}^\infty\frac{a^{n+m}}{(n+m)!} = ae^a-e^a+1
  37. U

    What is the sum of this series?

    Homework Statement If f(r) = r^3-5r^2+6r then \sum_{r=4}^{\infty } \dfrac{1}{f(r)} is The Attempt at a Solution I could decompose the above summation into something like this \dfrac{1}{3} \left( \sum \dfrac{1}{(r-2)(r-3)} - \sum \dfrac{1}{r(r-2)} \right) But from here I'm not...
  38. L

    MHB Find Minimal Sum of Distances: (1,2) & (4,3) on Axis OX

    find a point on the axis OX whose sum of distances to landmarks: (1, 2) and (4, 3) is minimal. Answer (2,0) (x-1)2+(y-2)^2 + (x-4)2+(y-3)^2 = D Y = mx I don't know if solve each distance apart or how i wrote??
  39. P

    Finding the sum of a Series that is converge or Diverge

    Homework Statement Determine whether the series is either Converge or Diverge, if it's convergent, find its sum ∑ from n=1 to ∞ of (1+2^n)/(3^n) Homework Equations The Attempt at a Solution Steps: 1) i replaced the (1+2^n) to just (2^n) and my equation behaves like ∑ (2/3)^n which...
  40. D

    Why do bound systems have less rest mass than the sum of its parts?

    Hi PF. This a fact well aware to just about anyone that has had even basic chemistry, but I'm having a hard time coming to an understanding as to why this must be true. So why? Also, if I knew that some box contained, say, a proton and an electron, could I ever know whether or not, inside...
  41. S

    What is the Sum of Discrete Sinusoids?

    Homework Statement Hi Everyone, I am trying to show why the given sum is zero. I am pretty sure it is zero. Homework Equations sin[8*\pi*n/5]+sin[12*\pi*n/5] n is an integer. The Attempt at a Solution n----sin[8*\pi*n/5]----sin[12*\pi*n/5] 0 ----...
  42. T

    How to Compute the Sum in the Stationary Distribution of a Markov Chain?

    Suppose we have a Markov chain with stationary distributions ##p_n=\frac{a}{nb+c}p_{n-1}## for ##n\in\mathbb{N}## where ##a,b## and ##c## are some positive constants. It follows that ##p_n=p_0\prod_{i=1}^n\frac{a}{ib+c}##. Normalisation yields...
  43. jdawg

    Summation of Infinite Series with Alternating Denominators

    Homework Statement Find the sum of the series: ∞n=1∑(6)/((2n-1)(2n+1)) Homework Equations The Attempt at a Solution S1=2 S2=2+(6/15) S3=2+(6/15)+(6/35) This is the part where I get a little confused. It looks like the denominator is getting bigger... So does it approach...
  44. znaya

    Engineering RCL circuit alternating current, calculate current sum

    Homework Statement Consider, in the circuit from the image, i1(t) = 5 cos(2t + 10º) v1(t) = 10 cos(2t - 60º). Find the value of the current ix(t). Options given: A: ix(t) = 9.9 cos(2t - 129.2º) B: ix(t) = 9 cos(2t - 29.2º) C: ix(t) = 99 cos(2t + 129.2º) D: ix(t) = 0.99 cos(2t +...
  45. anemone

    MHB Can This Infinite Series Be Summed?

    Evaluate $\dfrac{1}{3^2+1}+\dfrac{1}{4^2+2}+\dfrac{1}{5^2+3}+\cdots$
  46. anemone

    MHB Show the result of the sum of a series isn't a prime number

    Show that for an odd integer $m\ge 5$, $\displaystyle {m\choose 0} 5^{m-1}-{m\choose 1} 5^{m-2}+{m\choose 2} 5^{m-3}-\cdots+{m\choose m-1} $ is not a prime number.
  47. R

    Using a Fourier Cosine Series to evaluate a sum

    Homework Statement a) Show that the Fourier Cosine Series of f(x)=x,\quad 0\leq x<L is x ~ \frac{L}{2}-\frac{4 L}{\pi ^2}\left[\left(\frac{\pi x}{L}\right)+ \frac{\cos\left(\frac{3\pi x}{L}\right)}{3^2}+\frac{\cos\left(\frac{5 \pi x}{L}\right)}{5^2}+\dots\right] b) use the above series to...
  48. kq6up

    Exploring Infinite Series with Maxima: Finding Exact Sums with Analytic Programs

    Homework Statement From Mary Boas: Math for Phys. Sci. Ch1.15.20 20. By computer or tables, find the exact sum of each of the following series. a. \sum _{ n=1 }^{ \infty }{ \frac { { n } }{ { (4{ n }^{ 2 }-1) }^{ 2 } } } Homework Equations N/A. One is supposed to use an analytic...
  49. evinda

    MHB Upper-Lower sum of Riemann Integral

    Hello! (Wave) I am looking at the proof that if $f$ is integrable and $k \in \mathbb{R}$,then $kf$ is also integrable and $\int_a^b{(kf)}=k \int_a^b{f}$. The following identity is used at my textbook: $$U(kf,P)=\left\{\begin{matrix} k \cdot U(f,P), \text{ if } k>0\\ k \cdot L(f,P), \text{ if...
  50. paulmdrdo1

    MHB Solve for the Two Numbers: Sum 9, Difference 6

    can you help me solve this just using one variable the sum of two numbers is 9 and their difference is 6. what are the numbers? thanks!
Back
Top