Summation Definition and 627 Threads

  1. H

    Calculus problem with Summation I think?

    Homework Statement A line of buckets numbered 0,1,2... extends indefinitely to the left with an elephant behind each bucket. Initially, all of the buckets are empty but then peanuts start falling into bucket 0 at a rate of one per second for 2^12 seconds. Whenever 5 peanuts accumulate in a...
  2. C

    Simple summation, difficult inference. (game theory)

    hi guys, new user, long time lurker. the following simple proof is proposed with the highlighted summations. you do not need to know what the proof is of to answer my question (it is that the payoff for a skew symmetric game, rock paper scissors, is zero). i need help understanding how you...
  3. L

    Confusion over Einstein summation convention and metric tensors.

    My understanding of the Einstein Summation convention is that you sum over the repeated indices. But when I look at the metric tensor for a flat space I know that g^{λ}_{λ} = 1 But the summation convention makes me think that it should equal the trace of the matrix g_{μσ}. So it should...
  4. J

    Problem with summation, how did he find this result?

    Homework Statement Hi I was trying to understand an algorithm analysis problem and I came to this point: [PLAIN]http://img820.imageshack.us/img820/1834/unledytw.png can someone explain me what he did there? Is there any other step between that should have been written in order for...
  5. N

    Proving Summation of \frac{1}{i(i+1)} = \frac{n}{n+1}

    How can I show that \sum_{i=1}^n\;\frac1{i(i+1)}=\frac{n}{n+1} I've already figured out i can write it as \sum_{i=1}^n\;\frac1{i}-\sum_{i=1}^n\;\frac1{i+1} but as I'm a little drunk I can't figure out how to get from there to the formula. Sorry if I put this in the wrong sextion, but...
  6. S

    I'm trying to figure out what the summation notation of

    I'm trying to figure out what the summation notation of (1-x1)^θ * (1-x2)^θ * ...(1-xn)^θ would be for summation I know I need to convert this to a summation notation in order to solve my problem, but I can't figure out how to convert it. Any help will be appreciated.
  7. T

    How to interpret a Summation and Cartesian product together in a formula

    Hi all, \sum_{i=1}^n k_i \Pi_{i=1}^n O_i(\mu) How to interpret this equation.
  8. T

    Why Must the Real Part of \(c-a-b\) Be Positive in Gauss's Summation Formula?

    Why is the Gauss summation formula for complex parameters a,b,c: \displaystyle _2 F_1 (a,b;c;1) = \frac{\Gamma (c) \Gamma (c-a-b)}{\Gamma (c-a) \Gamma (c-b)} only valid for \text{Re}(c-a-b)>0,\;c\neq 0,-1,-2,-3,...?
  9. E

    Comp Sci C++: Simple summation program won't work correctly

    Homework Statement Write a C++ program to determine and print the sum of the series (1/3 + 1/6 + 1/9 + ... + 1/(3*n)) for a given value of n. In case you don't see the patter, the series can also be written as 1/(3*1) + 1/(3*2) +1/(3*3)+ ... + 1/(3*n). The value of n should be given...
  10. D

    Prove Summation Property: \displaystyle\sum\limits_{i=1}^n aij

    Homework Statement Show that the summation notation satisfies the following property: \displaystyle\sum\limits_{i=1}^n(\displaystyle\sum\limits_{j=1}^m aij) = \displaystyle\sum\limits_{j=1}^m(\displaystyle\sum\limits_{i=1}^n aij) Homework Equations N/A The Attempt at a Solution...
  11. H

    Q: What are the best study materials for understanding Ewald summation?

    I'm doing my masters thesis on ewald summation, I am searching for proper study materials for that... what I have is only papers(which you know doesnot explain everything they do!). It would be of great help if you can find me a few sources.. Please help. Thanks.
  12. V

    Evaluting Summation of Mutiplied Terms

    Homework Statement Evaluate the sums: \sum^{n}_{i=1}ia^{i} Homework Equations The Attempt at a Solution I'm assuming that because there's no limit or anything, the professor wants an equation. I know \sum^{n}_{i=1}i is \frac{1}{2}n(n+1) and \sum^{n}_{i=1}a^{i} is \frac{a^{n+1} - 1}{a-1}-1...
  13. K

    How can I use MATLAB to plot and sum values using vectors and matrices?

    Hi everyone, Could someone please tell me how to get MATLAB to do the following seemingly simple task.. j=1:3; k1=1:3; m=eye(3) plot(j,symsum((p8+k1(j)).*m(p8,j),p8,1,3)) or, k=1:3; plot(j,sum((k+k1(j)).*m(k,j))) Thanks for any suggestions, Kate
  14. E

    Mastering Partial Fractions for Solving Advanced Summation Problems

    Homework Statement Homework Equations The Attempt at a Solution Obviously I don't need a solution because it's right there. What I need to understand is what happened after the third equation sign and more importantly, how would I learn to solve these kinds of problems on my own. I looked at...
  15. V

    How does this summation equal \frac{n(n+1)(2n+1)}{6}?

    Homework Statement I'm not very proficient with LAtex, so I'll try to translate this mess the best I can. It's a summation \sum i2 (on the bottom, there would be an "i = 1") (on the top, there would be an "n") this summation equals \frac{n(n+1)(2n+1)}{6} In the summation, basically, "i"...
  16. Z

    Summation involving sine and cosine

    Homework Statement \omega^2=(2/M)\sum_{n>0}\frac{A\sin(nk_0a)}{na}(1-\cos(nKa)) A, a, and k_0 are constants, n is an integer. I need to find \omega^2 and \frac{\partial\omega^2}{\partial K}, but I have no idea where to start.Homework Equations Not sure, the stuff above.The Attempt at a...
  17. K

    Mathematica Mathematica: Please help me to improve the summation codes inside Do-Loop

    Dear all, I have a problem with regard to the summation which is done inside the Do-Loop iteration. I have attached the file which includes further information about the defintions, some examples and etc. Please help me to get the right codes in order to express totalu1, totalv1, totalu2 and...
  18. W

    Limit Process Summation Confusion

    Hi, I have been staring at this for a while. I under stand the process and can account for and reproduce every step of this problem EXCEPT I can nit figure out where the 6i/n coms from. I have included the equation and the issue is highlighted in yellow. Please explain... this is the last...
  19. S

    Find the maximum value of a summation

    Hi, What is the maximum value of the given summation in terms of k, l and N ? max_{0\leq x \leq k} \sum_{(l_1,l_2)\in A} \frac{N!}{(N-l_1-l_2)!l_1!l_2!} x^{l_1}(k-x)^{l_2}(1-k)^{N-l_1-l_2} where A=\{(l_1,l_2)|l_1,l_2 \in \{0,1,2,...,N\} and l_1+2l_2=l\} and 0<k<1. Thanks a lot for your...
  20. M

    Find the Summation Notation and the Radius of Convergence

    Homework Statement Find the Summation Notation and Radius of Convergence of this series. 5, x, 10, x, ... The Attempt at a Solution I don't know how did they come up with that equation.. But the summation seems right.. Can anyone tell me how did they arrive with that equation? I've tried...
  21. I

    Sum of n Terms of 7/(1.2.3) - 17/(2.3.4) + Series

    Find the sum of n terms of the series: 7/(1.2.3) - 17/(2.3.4) + 31/(3.4.5) - 49/(4.5.6) + 71/(5.6.7) - ...I know how problems like the following are solved : 1. 1/(1.2.3) + 2/(2.3.4) + 3/(3.4.5) + ... 2. 3/(1.2.4) + 4/(2.3.5) + 5/(3.4.6) + ...What will be the general term of the required...
  22. S

    How Do You Calculate This Double Summation?

    Hi, Can every body solve this problem in terms of a and b . e^{-(a+b)}\sum _{n=0}^{\infty} \frac{a^n}{n!} \sum_{m=0}^{n}\frac{b^m}{m!} Thanks in advance for your participation.
  23. J

    Periodicity of the summation of two functions

    Homework Statement show whether or not x(t) = cos(t) + sin(\sqrt{2}*t) is periodic The Attempt at a Solution the first period is T1 = 2\pi the second period is T2 = \frac{2\pi}{\sqrt{2}} how can I determine whether it is periodic or not? in my book(about signals...
  24. A

    Infinite summation for x^(1-x)

    Along with some friends, i was trying to calculate the end product of a series(x^(1-x)). I for a finite value, i got a number close to arcsinh(SQRT 6), and by comparing the functions i believe it converges at infinity. However, i am unable to 100% prove this, and i am asking if the summation is...
  25. K

    Mathematica Mathematica: Summation in the Do-Loop

    Dear all, Iam trying to get the right codes so that the summation could be done in the Do-Loop function using Mathematica. The problem is that I could not get the summation for sumU1 and sumV1 to start from 1 using my codes as attached (Summation2.nb). Please help me to improve the...
  26. P

    How Many Terms to Achieve a Difference of 0.00001 in Infinite Summation Series?

    Hi, First term is 10 and common ration is 0.02. We have to find the number of terms necessary so that the difference between the infinite summation and the sum of those terms differ by 0.00001. This is what I did: (U1 - r) / (1-r) - (U1(rn-1)) / (r - 1) = 0.00001 I get: - 0.2n + 10 =...
  27. M

    Summation of sines and cosines questions

    This is not a homework question per say, but rather a question I have about a text I am reading. In the text, they have defined \sum E_{n} Cos \left( \frac{2 \pi X_{n}}{\lambda} \right) = E Cos \phi If this is the case, is it fair to say that \sum E_{n} Sin \left( \frac{2 \pi...
  28. Y

    Find the Fourier Series for f(x)=x^2 evaluate f(0) and show that the summation

    Find the Fourier Series for f(x)=x^2 evaluate f(0) and show that the summation \sum^{\infty}_{n=1}\frac{1}{(2n-1)^2}=\frac{\pi^2}{8} The first part of this problem asked that I find a_{n} and b_{n} Since x^2 is an even function b_n=0 and for a_n I got \frac{4(-1)^2}{n^2} for a_0 I got...
  29. B

    How to simplify cos^2(kx) using trig identities?

    Homework Statement Given \begin{equation} x[n]=A\cos(\frac{2\pi n}{M}+\phi) \end{equation} Evaluate(average power of a sinusoidal digitally sampled signal) : \begin{equation} P_x=\frac{1}{N}\sum_{n=0}^{N-1}{|x[n]|}^2 \end{equation}Homework Equations Trig Identities...
  30. A

    Solving Summation Problem: 1/1! + 2/2! + 3/3! + 4/4!...

    Hello, i have been trying to solve a summation question for a while, and I'm not too much of an expert at the subject, so i couldn't figure it out. it is the sum of n/n! in which n takes the value from one to infinity. In other words, just 1/1! + 2/2! + 3/3! + 4/4!... Well, firstly, does the...
  31. J

    Finding summation when given a fourier expansion of a function

    Homework Statement I have a function f(x) = x^2/4 for |x|<π I have the Fourier series of this function which is and I need to prove that The Attempt at a Solution I tried to use dirichlet for x = 0 but I get -pi^2/3
  32. F

    MATLAB Gamultiobj with double summation help

    how can i use gamultiobj or ga, I've input of (i, j) matrix and i want (i,j) output i've equation to solve with ga f = sumation from i to class[ sumation from j to rows(yij * log(pij)))] how to solve with ga fun f = funGa1(Pij,Yij,class,rows) f = -...
  33. J

    Mathematical induction w/ Summation question

    Homework Statement Summation of i(i + 1) (with i going from i = 2 to i = n-1) = n(n-1)(n=1) / 3 a. Write P(2). Is P(2) true? b. Write P(k) c. Write P(k+1) d. Prove by mathematical induction that the formula holds true for all integers n \geq 2 Homework Equations...
  34. K

    Mathematica How can I fix the warning for solving summation in Mathematica?

    Hi everyone, I have these warning solving summation: ************************************************* In[1]: f[m_, n_] := 2 n + 3 m; In[2]: g[m_, n_] := Sum[f[m, n], {m, 1, m, 2}, {n, n, 1}]; In[3]: g[1, 1] During evaluation of In[3]:= Sum::itraw: Raw object 1 cannot be used as an...
  35. K

    Partial Differentiation of Summations for Finding Derivatives

    Homework Statement By differentiating the summation, show that ∂/∂b₀ ƒ(b₀ , b₁) = -2 ∑_(i=1)^n (y₁ - b₀ - b₁x₁) Homework Equations the ‘derivative of the sums’ equals ‘the sum of the derivatives’: The Attempt at a Solution How would we partially differentiate a summation...
  36. mnb96

    Find Closed-Form Expression for Summation of n^2

    Hello, could anyone give me a hint on how to find a closed-form expression for the following summation: Q_N = \sum_{z=1}^N z^2 where z are positive integers from 1 to N. Thanks.
  37. M

    Summation of Series: Is the Radius from -∞ to ∞?

    Homework Statement sum ((x-1)^(2n-2))/((2n-1)!) n=1..infinity? after doing the ratio test, i found that the radius is from negative infinity to infinity (converges for all x). is this right? if not can you steer me in the right direction, please. Homework Equations The Attempt...
  38. P

    Solving Infinite Summation - Peter G.

    I posted this initially in Pre-Calculus, but, seeing several people with similar doubts have posted this question here, I'll do the same, even though I haven't started Calculus I am investigating the sum of infinite sequences. such that: t0 = 1 and tn = (x ln (a))n/n! They tell me to...
  39. P

    Investigating Infinite Summation: Calculating Sn 0-10

    I am investigating the sum of infinite sequences. such that: t0 = 1 and tn = (x ln (a))n/n! They tell me to first consider the following sequences of terms: 1, (ln 2)/1, (ln 2)2/2x1, (ln 2)3/3x2x1 They then ask me to calculate the sum Sn of the first n terms of the sequence for when...
  40. F

    The proof of convergence. I am confused with the summation

    Homework Statement Prove\; that\;if\;\sum_{n=1}^{\infty} a_n \;converges,\;then \lim_{n\to\infty}a_n = 0 Book solution s_n= a_1 + a_2 +...+a_n s_{n-1}= a_1 + a_2 +...+a_{n-1} a_n=s_n-s_{n-1} Then they did a few limits, and proved that the difference is 0. BUt that is not my...
  41. K

    Limit of Summation: Find Solution

    Homework Statement Find the limit n to Infinity of summation (i=1 to n) 1/n * ((i/n)^2) The Attempt at a Solution I thought it was zero at first because 1/n goes to zero but apparently that's not right. I also tried to convert to an integral and got integral of i^2/n^2 which equals...
  42. T

    Understanding Summation: S_X and S^2_X

    Does \displaystyle S^2_X = \sum^n_{i=1} (X_i - \overline{X})^2 mean \displaystyle S_X = \sum^n_{i=1} (X_i - \overline{X}) (X is a random variable here) and is this true of summations in general? i.e. does \sqrt{\sum X_i^2} = \sum X_i ? I thought it'd be \sqrt{\left( \sum...
  43. C

    Summation of alternating series

    Homework Statement Determine the value of the sum \sum_{n=1}^\infty \frac{(-1)^n}{1+n^2} I have determined it trough the use of Fourier series, but does there exist another way to do it?
  44. H

    Convergent Sum of Sine Series with Added Term for Continuity

    Find the convergent sum and find the sum of first five terms \sum_{n=1}^{\infty} \frac{sin(nx)}{2^nn} from 1 to infinity. I have found so far that: \sum_{n=1}^{\infty} \frac{sin(nx)}{2^n} = \frac{2sin(x)}{5-4cos(x)} I am not sure how to consider the \frac{1}{n} term. Can someone please help?
  45. B

    Solving for a variable in the partial derivative of a summation

    I'm trying to find the partial derivative of Q with respect to w0 and then set it equal to 0 and solve for w0. Finding the partial derivative was easy, but once I've got it, I'm having a hard time getting w0 by itself. Here's the original equation: Q(w_{0},w_{1},w_{2},w_{3})=\sum\left(y_{i}...
  46. G

    Advanced EM problem involving summation of 1/Cosh

    We solve Poisson's equation in cartesian coords for a region bounded by planes forming a box. Some of the planes are grounded. The lengths of the box are L1, L2, L3. There is no charge distribution. Let a=mPi/L2 b=nPi/L3 The solutions goes like: sinh(sqrt(a^2 +...
  47. M

    How do we convert a summation to integration?

    When converting a summation of the form \sum x_i y_i to integration, how do we know if it's \int x dy or \int y dx At first I thought they're equivalent but obviously that's only true for a linear function with no constant offset. I kind of see integration as a better...
  48. S

    Series Summation: Solving for r^2 with (2r+1)^3 and (2r-1)^3 Equations

    Homework Statement Given that \left(2r + 1\right)^{3} - \left(2r - 1\right)^{3} = 24r^{2} + 2, show that \sum r^{2} = \frac{1}{6}n(n+1)(2n+1). Homework Equations No idea! The Attempt at a Solution
  49. M

    Is the Summation of lg k in log(n!) Equal to Theta (n lgn)?

    Homework Statement Prove that the following is true: n \Sigma lg k = \Theta (n lgn) k=1 Homework Equations the lg in this case is base 2 The Attempt at a Solution i don't kno how to apply geometric or arithmetic progression to the 1st part i was trying to substitute for k but that wasnt...
  50. E

    Fourier Series - Summation to Integral

    Homework Statement My question involves the mid-point in deriving some of the equations to solve Laplace's equation in rectangular coordinates. The question may no make sense as it isn't problem specific. I can provide boundary values if necessary - just let me know. Homework Equations...
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