Summation Definition and 610 Threads

\sum^k_{n=1}e^{-n\sum^k_{n=2}...e^{-n\sum^k_{n=k-1}e^{-n}}} Can anyone help me find out if this converges and if so how to calculate the sum? I don't have an idea on how to even start. This is not homework

Hello, I think I am fundamentally confused with summation convention. For example, if I have \epsilon_{ijk}x_j\delta_{jk} Can I sift the levi civita and get \epsilon_{ijj}x_j=0 or sift x and get \epsilon_{ijk}x_k\not=0 Each gives a different answer. What mistake...

I am working on a problem that uses the notation: \sum_{i,j=1}^n A_{i,j} Where A is an (n x n) matrix. I am a little unsure of what the summation is over, due to the odd notation "i,j = 1". My first guess is that this is shorthand for \sum_{i=1}^n \sum_{j=1}^n A_{i,j} But I...

So I am trying to derive a formula from one of the standard summation formulas except starting at a different index. So if I have the series.. \sum i = \frac{n(n+1)}{2} Where "i" runs from 1 to n. (I don't know how to put it in the code.) If I want to make the series start from zero, I...

hi i am just reading some notes on tesor analysis and in the notes itself while representing vectors in terms of basis using einstein summation notation the author switches between subsripts and superscripts at times. are there any different in these notation. if so what are they and when should...

how do I evaluate \sum_{k=0}^d \binom{n+d-k}{n} ?

what is the sum of this series ?? \sum_{n=0}^{\infty}n^{b}e^{ian} for every a and b to be Real numbers from the definition of POlylogarithm i would say \sum_{n=0}^{\infty}n^{b}e^{ian}= Li_{-b}(e^{ia}) however i would like to know if the sum is Cesaro summable and what it would be...

Homework Statement \sum^{n}_{r=1}(\lg \frac{2^r(r+1)}{r})=\sum^{n}_{r=1}[\lg 2^r+\lg (r+1)-\lg r] Homework Equations The Attempt at a Solution i found the answer to be (2^n-1)\lg 2 +\lg (n+1) Am i correct , or it can be further simplified ? Thanks .

Homework Statement A set contains numbers from 1-100. What is the least non-negative value that one can form by putting a + or - in front of each number, and summing the values?Homework Equations there are a few general summation formulas which I know... The Attempt at a Solution The...

Homework Statement Basically need to use einstein's summation convention to find the grad of (mod r)^n and a.r where a is a vector and r = (x,y,z) Homework Equations The Attempt at a Solution Not sure where to begin really.. :S grad (mod r)^n= (d/dx, d/dy, d/dz) of root (X1^2...

Hi, I've been looking through my algorithms book/notes and I've come across this summation I'm not quite sure how they got to. \sum^{lgn - 1}_{i = 0}\frac{n}{lgn - i} = n\sum^{lgn}_{i = 1}\frac{n}{i} where lgn = log_{2}n, it's just to make it simpler any clue? cheers,

Homework Statement It can be shown that ∑(n=1) to (n=∞) of 1/n² = π²/6 use this fact to show that ∑(n=1) to (n=∞) of 1/(2n-1)² = π²/8 Homework Equations The Attempt at a Solution

Hello, I am having difficulty approaching this problem: Assume that K, Z_1, Z_2, ... are independent. Let K be geometrically distributed with parameter success = p, failure = q. P(K = k) = q^(k-1) * p , k >= 1 Let Z_1, Z_2, ... be iid exponentially distributed random variables with...

\sum_{i=1}^{n} i is the sum of all numbers between 1 and n. I'm trying to find one for odd numbers where you need to find the sum of all odd numbers between 1 and n. I tried 2n+1 which worked, only for first n numbers, not for numbers 1 to n. Thanks for the help.

Hello all, In the book "A First Course in General Relativity" by Schutz (1985 Edition) in chapter 2 there is a problem concerning summation that has me confused. Note: This is not homework, just an interest of mine. The given quantities are: A = (5,0,-1,-6) B = (0,-2,4,0) C = [ 1 0 2 3...

Homework Statement This isn't really a homework question, but something I've been wanting to know out of curiosity in David Griffiths' Introduction to Electrodynamics. On pages 131 and 132, there is a Fourier series, V(x,y) = \frac{4V_0}{\pi}\sum_{n=1,3,5...}\frac{1}{n}e^{\frac{-n \pi...

Hello this is something that just crossed my mind: For every real sequence (a_n)_{n\geq 1} we can define the generating function A(z)=\sum_{n=1}^\infty{a_nz^n}. and this definition suggests that we can compute the sum of the sequence by evaluating A at 1: A(1)=\sum_{n=1}^\infty{a_n}...

If I have ∑(k xi + j yi)...how will I apply the distributive law on it?...I mean how do you split this notion?

Homework Statement find the sum for \sum_{k=1}^{\infty} kx^{k} Homework Equations \sum_{k=0}^{\infty} x^{k} = \frac{1}{1-x}; -1 < x < 1 The Attempt at a Solution \sum_{k=1}^{\infty} kx^{k} = \sum_{n=0}^{\infty}(n+1)x^{n+1} = x\sum_{n=0}^{\infty} (n+1)x^{n} = x \frac{d}{dx}...

\sum_{k=0}^{\infty}a_{k}(k+r)(k+r-1)x^{k-1} I need to get my x term to look like xn. If I set n = k-1, then that makes my index start at n = -1, which is silly. What can I do?

Homework Statement Define Tn as the sum of the first n terms, for various values of a and x, e.g. T9(2,5) is the sume of the first nine terms when a = 2 and x = 5. The first n terms are 0-10, including both 0 and 10. Homework Equations T0=1, T1= (xlna)1/1, T2= (xlna)2/2!, T3=...

Homework Statement Ok I have the answer to a question, all the working is given, however, I'm having trouble following it. Homework Equations http://img695.imageshack.us/img695/426/answer.jpg The Attempt at a Solution I am completely lost, could someone please explain the steps that have...

Homework Statement Let lim n-> ∞ a_n = L. Then, let f(x) = ∑ from n=0 to ∞ of (a_n)(x^n). Show that the lim x-> 1 (1-x)f(x) = L. Homework Equations The Attempt at a Solution This one is pretty far over my head. I know at some point you're supposed to use Abel/SBP, but here is what I have so...

Please look at the attachments (for the problem and my work) , thank you. The answer from the book is 2.84 but I got 14.4. How come? My problem is #23

I hope can someone clarify this for me. I have a sequence f(of n) which is like this: fn(x) = 0-- if--x<\frac{1}{n+1} is = sin^2(x/pi)--if--\frac{1}{n+1}<=x<=\frac{ 1}{n} is = 0--if--\frac{1}{n}<x (the - are for spaces because I don't know how to do it. Nothing is negative) Then...

Homework Statement I'm just not sure how to change the operators in summation, can anyone help? Let s_{n}=\sum_{k=1} ^n ((-1)^{k+1})/k what is s_{2n}?Homework Equations s_{n}=\sum_{k=1} ^n ((-1)^{k+1})/k The Attempt at a Solution s_{2n}=\sum_{k=1} ^{2n} ((-1)^{2k+1})/2k or...

Homework Statement what is the summation of a function where n=1 to n=infinity? For example, given a function sin[(pi)nt]. Homework Equations The Attempt at a Solution I asking how I get that I do not know what should I do

Just got a "thought experiment" question from a colleague. The question, as phrased was: If an audio signal was composed by adding all of the frequencies in the audible range, what would it sound like? I thought it was interesting, so I attempted to solve it by integral. My calculus skills...

How to say ... Hi ... I'm doing a small presentation and I was wondering how I would say the following summation: \sum_{0<i_1<...<i_n<p} \left(\frac{i_1}{3}\right) \frac{(-1)^{i_1}}{i_1 i_2 \cdot \cdot \cdot i_n} where \left(\frac{i_1}{3}\right) is the Legendre symbol, n is a positive odd...

Hey guys and gals, While this technically isn't homework, I figured this is the place to post. I am working over a problem and I am at a point in the solution that has me a bit stumped. Perhaps someone may provide some guidance. In acoustics, we run into the problem of a radiating body...

I just thought I would share this, I was about to ask you fine people how to do this when I realized the square root of the sum of progressive to regressive data equals the highest point. I.E. 1+2+3+4+5+6+5+4+3+2+1=36 6^{2}=36 and I tried this a few times and the results were the same...

Homework Statement n+1 , n \sum (nCk-1) f(x)g(x) + \sum (nCk) f(x)g(x) k=1 , k = 0 (for first and second summations respectively) I can't just say that that is equal to: n+1 \sum (n+1 C k) f(x)g(x) k=0...

Homework Statement I want to calculate a sum (where the end value is in the sum), eg: \sum^{n-1}_{i=1}{2i+n} Homework Equations I don't want to 'split' the sum, i just want to write this. The Attempt at a Solution syms i n for n=1:5 for i=1:n-1...

I came across this approximation in a book. I am not sure why this approximation is valid.. \frac{1}{N}\sum_{n=0}^{N-1}n.sin[4\pi f_o n + 2\phi] \approx 0 f_o is not near 0 or 1/2 Saurav

Homework Statement Prove by induction the following summation formula: \frac{1}{1\1*2} + \frac{1}{2*3} + ... + \frac{1}{n(n+1)} = 1 - \frac{1}{n+1} n \geq 1 Homework Equations - The Attempt at a Solution Inductive step: 1. \frac{1}{1*2} + \frac{1}{2*3} + ... + \frac{1}{n(n+1)} +...

Hi everyone. I hardly remember the fomulas of summation of sequence. I got this problem. {\frac{1}{8}}\sum^{\infty}_{n=2}n({\frac{3}{4}})^{n-2} The result is 2.5. How can I solve this problem? Thanks all. :)

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