Summation Definition and 627 Threads

Homework Statement Using the Einstein summation convention, prove: A\bulletB\timesC = C\bulletA\timesB Homework Equations The Attempt at a Solution I tried to follow an example from my notes, but I don't entirely understand it. Would it be possible to find out if what I've...

Summation Problems! Please Help! My geography prof assigned these... believe it or not. Its a quiz and its worth 5% of our mark. 1) Σi^4 = 1^xi Variables - n=4 x1=1 x2=6 x3=9 x4=17 (i think its 4) 2) (Σi^4=1^xi)^2 n=4 x1=3 x2=10 x3=9 x4=12 (i think this one is 4 also) 3) Σi^2= 1Σj^2 =...

\sum\frac{1}{(2j-1)^2} This fgoes from j=1 to infinity. I was just wondering if somebody could calculate and show all working to show the value that this function converges to as i have no idea of how to do this? Thanks for your help

Let k and n \le X be large positive integers, and p is a prime. Define F(X,n) := \sum_{\substack{k^2+p = n\\X/2\le p<X\\\sqrt{X}/2 \le k < \sqrt{X}}}\log p Q(n) := \sum_{k^2+p = n}\log p.Note that in Q(n), the ranges of k and p are unrestricted. My question is: I know that F(X,n) and Q(n) can...

Homework Statement Evaluate the following sums, implied according to the Einstein Summation Convention. \begin{array}{l} \delta _{ii} = \\ \varepsilon _{12j} \delta _{j3} = \\ \varepsilon _{12k} \delta _{1k} = \\ \varepsilon _{1jj} = \\ \end{array} The Attempt at a...

Homework Statement This is kind of a question regarding summation. All logs are to base 2. Given A=\sum_{n=2}^{\infty}(n\log^{2}(n))^{-1} Why does the the Author get \sum_{n=2}^{\infty}\frac{\log A}{An\log^{2}(n)}=\log A ? Homework Equations The Attempt at a...

Hi guys, sry if i asked a silly qns. Is the below equivalent is true?

\sum_{n=1}^{\infty}n^{-2}=\frac{\pi^2}{6} I'd like to know how to prove this summation. And if possible, what is the significance of having \pi in the answer?

\sum_{n=1}^{\infty}(-1)^{n}\frac{e^{-\frac{1}{nx}}}{n} Where 0<x<oo. I'm looking for a closed form/ closed representation for this series [I was thinking something like a polylogarithm or dirichlet eta function combination might work]. Any ideas or suggestions would be much appreciated.

Can anyone explain this property of shifting the index on the summation notation? I'm reading a book and came across this which has confused me. I don't see how these are equal: \sum_{k=1}^n \frac{1}{k(k+1)} = \frac{1}{2} + \sum_{k=2}^{n+1} \frac{1}{k(k-1)} It's part of an explanation that...

The problem is to prove the following: \sum_{m>0}J_{j+m}(x)J_{j+m+n}(x) = \frac{x}{2n}\left(J_{j+1}(x)J_{j+n}(x) - J_{j}(x)J_{j+n+1}(x)\right). Now for the rambling... I've been reading for a while, but this is my first post. Did a quick search, but I didn't find anything relevant. I could...

I need to find a way to sum/ a closed form representation for: \sum^{N}_{n=1}\frac{\Gamma(n-s)}{\Gamma(n+s)} 0<Re(s)<1 Thanks for the help in advance.

This is not really a homework problem, but I'm studying a text, and I came across this: http://img198.imageshack.us/img198/4586/sumh.jpg I know how to get that fraction with the exponents in it (using a summation formula). But for the life of me, I can't figure out how to manipulate that...

Can someone give me an explanation or possibly a proof that \int^{a}_{b}f(x)dx= \displaystyle\lim_{m\to\infty}\sum^{m}_{k=1}f(x^{*}_{k})\Delta x

I need to know if the following series converges: ∑(k=1 to k=oo)[(((-1)^k) ζ(k))/(e^k)] The problem is that zeta(1)=oo; however, the equation satisfies the conditions of convergence for an alternating series [the limit as k->oo=0 and each term is smaller than the last.] Any thoughts?

How would you say this in words?

I am trying to understand the derivation of the Poisson's sum formula. Wikipedia's article is like crosswords to me. I checked mathworld's take on it. It looked simple, but it stated that the equation is derived from a more general result without stating or proving that general result. Here's...

Hello, Can we write a summation of exponentials, as a multiplication of exponentials? Regards

2008 Summation (-1)^{i} \frac{i^2+i+1}{i!} i=1 I guess I am suppose to apply the summation rule and i got (-1)^{i} \frac{n(n+1)(n+2)+3n}{3i!}

Homework Statement f(x) = \frac{1-cos(X^2)}{x^3} which identity shoud i use? and tips on this type of questions? once i can separate them, then i'll be good thanks!

Hello, If we get a summation \sum_{r=a}^{b}, where a > b, how to treat this summation? Regards

Hey all, The way I was taught GR, the summation convention applies on terms where an index is repeated strictly with one covariant, one contravariant. But reading through a translation of Einstein's GR foundations paper just now it looks like the index placement doesn't matter (I've seen it...

Does anyone know if there is a summation formula to find the sum of an expression with n as an argument in a trig function? I'm asking this because I'm learning about Fourier series/analysis but it seems that once we have the Fourier series we only sum for n=1,n=2,n=3... We never sum there...

I came across this yesterday when I was looking for equalities between the sums of two summations. I'm not sure if this is part of a proof or what.

i need to write this into MATLAB http://www.engin.umich.edu/class/bme456/ch10fitbiphasic/biphasfit19.gif which i have done here: uj = (-sig/Ha)*(xj-(((2*h)/(pi^2))*((((-1)^n)/((n+1/2)^(1/2)))*sin((n+1/2)*((pi*xj)/h))*exp(((-Ha*ko)/(h^2))*((n+1/2)^2)*(pi^2)*t)))); how do i vary n...

Hey, I have a general question about summations. Is there any steadfast rule for calculating, or obtaining a sometimes-calculatable function for, the derivative of x, where x is the upper bound of summation in a simple summation expression (the summation of f(n), from n = 1 to x)? If not...

What is the general formula for a1 + a2 + a3 + ... + an = A, where all the variables a_i and A are non-negative integers.

I know how to write it out in the general window, but not in the graphing window (there's no summation option in the graph feature). Is there a way to import it or another way?

Hi, This is to do with my research. While deriving some theory, I got an equation as follows. \lim_{n\rightarrow\infty}\sum_{i=1}^n\frac{R^2}{R^2+(4a\,i-2\,k)^2-(4a\,i-2\,k)\,\sin(\gamma)} Never mind what R, a, k, and \gamma are. They are all constants. What I would like to do is to get a...

Hey everyone, I need some help trying to figure out how to find the summation of n \sum_{}^{\6}i^p i=0 I was looking on the web and found on Wikipedia this formula off the http://en.wikipedia.org/wiki/Summation" page. It looks like this assuming I copied it right (ignore the periods)...

Homework Statement Define I(x)= I( x - x_n ) = { 0 , when x < x_n { 1, when x >= x_n. Let f be the monotone function on [0,1] defined by f(x) = \sum_{n=1}^{\infty} \frac{1}{2^n} I ( x - x_n) where x_n = \frac {n}{n+1} , n \in \mathbb{N} . Find \int_0^1 f(x) dx ...

hello guys, I have tried to evaluate \Sigma e-an2 so many times, but I didn't get it. where a is just a constant and summation begin from n=1 to infinity. I know that \Sigmaen is just geometric series which is equal 1/(1-e) But when n changes to be n2, I have no ideas how to do that. If...

Fourier series summation...help! Basically, i need to show that... 2 + sum (m=1 to n) [4(-1)^m . cos(m.pi.x)] = 2(-1)^n.cos((n+1/2)pi.x)/cos((pi.x)/2) Any ideas?

I have been trying to solve Summation as Limit to Infinity type of questions but there are hardly a few examples I could find in my book I know the general method for \lim_{n \rightarrow \infty } \frac{1}{n}\Sigma_{r=A(x)}^{B(x)}f\frac{r}{n} where r/n is replaced by x and 1/n by dx, the limits...

I am having trouble understanding how to find the limit of a summation. I know the formulas and properties but cannot seem to simplify them into a rational form becuase i have never been good at simplifying rational expressions and if there is an easier way to solve them. I enjoy Summation math...

Find an N so that N 0< e-\sum 1/n! < 10^-14 n=0 I seriously don't know how to go about this problem. Please help me out. Thanks

Homework Statement Let f(n) = 1/2 + 1/3 + ... + 1/n Show that f(n) is not an integer for any positive integer n The Attempt at a Solution I think that rearraning/breaking down the statement might be easier than applying a theorem since it seems like a simpler problem. Simply...

This equation comes out of deriving the canonical partition function for some system. However, the question is more math based. I am having trouble understanding the simplification that was performed in the text: ∑ from N=0 to M of: (M!exp((M-2N)a))/(N!(M-N)!) supposedly becomes...

Homework Statement \Sigma^{4}_{k=0} \stackrel{1}{k^{2}+1} Homework Equations I would imagine it has something to do with this property \Sigma^{n}_{i=1} i^{2} = \stackrel{n(n+1)(2n+1)}{6} The Attempt at a Solution So at first I thought I could bring k^{2}+1 to the top by...

Is there a way to simplify this sum to a generalized function? Would I have to use the gamma function? \sum^x_{k=0} ({t \choose {2k}}/(2k+1)^y) where x and y are constants This is not homework.

Hi, there is a good expression for \sum_{s}{u_s(\vec{p})\bar{v_s}(\vec{p})} ? Thank you

write out the following sum and compute where possible \sum 3 x =0 (x2 + 2x + 2) is that clear?

Please help me in solving the problem, find the sum Sum{r=2 to infinity} (von Mangoldt(r)-1)/r Your help is appreciated.

I am wondering whether the following expression can be simplified sum of( (p^n) / (n!) ) from n=1 to n=n.

I feel so silly asking this question, but is (the summation is over n1 from 1 to infinity. I have no idea how to type it with the latex) \sum(x1^n1)/n1!*(x^(n-n1))/(n-n1)! = lim(_{n1 \rightarrow \infty}) (1 + x/n1)^n1 * lim(_{n1 \rightarrow \infty}) (1 + x/(n-n1))^(n-n1) = exp(x1)*exp(x2)...

Okay, this is a derivation from Relativistic Quantum Mechanics but the question is purely mathematical in nature. I presume all you guys are familiar with the Levi-Civita symbol. Well I'll just start the derivation. So we are asked to prove that: [S^2, S_j] =0 Where...

Q1. f is a continuous real valued function on [o,oo) and a is a real number Prove that the following statement are equivalent; (i) f(x)--->a, as x--->oo (ii) for every sequence {x_n} of positive numbers such that x_n --->oo one has that (1/n)\sum f(x_k)--->a, as n--->oo (the sum is taken...

Hi, I'm a beginner in C++. I wan't to write this program: Write a program that asks the user to enter n numbers –where n entered by the user- and calculates the sum of even numbers only. main function asks the user to enter n and then calls the recursive function Sum to read the values...

[SOLVED] Seperating a Summation problem. Homework Statement The Problem: Separate a sum into 2 pieces (part of a proof problem). Using: X= \sum^{n}_{k=1}\frac{n!}{(n-k)!} Solve in relation to n and X: \sum^{n+1}_{k=1}\frac{(n+1)!}{(n+1-k)!} Homework Equations ? The...

can someone help me explain how to get 32 from the summation? thanks in advance..