Summation Definition and 610 Threads

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...

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...

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.

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...

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

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...

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"...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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 =...

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...

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...

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...

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...

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

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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?

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?

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}...

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...

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

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...

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...

Hi, I've been trying to make another expression for, m \sum(k!) = f(m) k=0 I did one expression that is, f(m) = 2(3(4(5...((m-1)(m+1)+1)...+1)+1)+1)+1 For instance, f(4) = 2(3(4+1)+1)+1 Can you hint me on finding a finite expression for the above expression? Thanks for help.

Homework Statement Let \vec{A}(\vec{r})and \vec{B}(\vec{r}) be vector fields. Show that Homework Equations \vec{\nabla}\bullet(\vec{A}\vec{B})=(\vec{A}\bullet\vec{\nabla})\vec{B}+\vec{B}(\vec{\nabla}\bullet\vec{A}) This is EXACTLY how it is written in Ch 3 Problem 2 of Schwinger...

I'm a little stuck here... I need to write this in the summation notation, and then find and prove a formula in terms of n, using induction :3+7+11+...+(4n-1) I know that the summation notation is n +--- \ / 4i-1 +--- i=1 but I have no idea how to...

Homework Statement \sum_{i=0}^{n} i^{p} = \frac {(n+1)^{p+1}}{p+1} + \sum_{k=1}^{p} \frac {B_{k}}{p-k+1} (^{p}_{k}) (n+1)^{p-k+1} where Bk is a Bernoulli number. There is no actual question here I would just like to know if this formula is for sums of i to any power, of course...

Hello everybody, Are there any generalization of this summation \sum_{k=1}^{n}k^{a} for a>3? Thanks for your responses.

1. how do i find the period of summation of some function ie: 2^-k or cos(pi k) multiplied by some complex exponential ei7kt ie: f( t ) = \sum 2-kei7kt 2. does anyone know the formula for finding the period of summations of complex exponentials? note this is for fourier 3. would i say that...

Homework Statement Find and prove a formula for sum{ (m1 choose r)(m2 choose s)(m3 choose t) } where the sum is over all nonnegative integers r, s, ant t with fixed sum r + s + t = n. Homework Equations The Attempt at a Solution I first attempted to find the number of combinations of r...

Homework Statement Prove that \sum^{l}_{k=0} n \choose k m \choose l-k = n+m \choose l Hint: Apply the binomial theorem to (1+x)n(1+x)m Homework Equations The Attempt at a Solution I apply the hint to that thing to get \sum^{n}_{j=0} n \choose j x^j \sum^{m}_{k=0} m \choose k...

Homework Statement "Aim: In this task, you will investigate the sum of infinite sequences tn, where tn = {\frac{(x\ln{a})^n}{n!}}, and t0=1 Consider the sequence when x=1 and a=2. Using technology, plot the relation between Sn (the sum of t0+...+tn) and the first n terms of the sequence for...

Homework Statement \sum\limits_{j=0}^\infty \binom{j}{r} p^r (1-p)^{j-r} (1-q) q^j where p and q are between 0 and 1, and r is a positive integer Homework Equations The Attempt at a Solution since \binom{j}{r}=\binom{j}{j-r} we can rewrite the summation as (1-q)\sum\limits_{j=0}^\infty...