Summation Definition and 627 Threads

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...

prove that: \sum_{m=0}^{q} (n-m) \frac{(p-m)!}{m!} = \frac{(p+q+1)!}{q!} (\frac{n}{p+1} - \frac{q}{p+2} ) using induction

I know this should be easy and the answer will be glaringly obvious in hindsight but my brain is fried and I can't for the life of me figure this out. My problem is this I have a function as follows; V = \sum\lambdai,j,k hihjhk (summation over i,j,k where i,j,k = 1,2,3) I can't work...

It isn't homework, it's in a textbook and I'm having trouble with it. When r=1, summing to n the series of r^3 = (n^2)/4 (n+1)^2 Show that when r = (n+1), summing to 2n = (n^2)/4 (3n+1)(5n+3) What order do you start the summation, and how do I begin?

Homework Statement I am solving some convolutions, and i have come to these solutions. a)\sum2k, summing from -\infty to -1 b)\sum2k, summing from -\infty to n , where n <=-1Homework Equations the geometric series summation formula, from 0 to N \sumak = 1-aN+1 / 1-a , summing from 0 to N The...

Homework Statement Summation from 1 to infinity of 1.05^n/n^5 Homework Equations The Attempt at a Solution Lost. I'm not sure if the ratio test would apply here.. convergence tests are definitely not my strong point!

Homework Statement Use the Summation Identity to count the cubes of all integers sizes formed by an n by n by n assembly of cubes. Homework Equations Summation Identity: Sum [from i = 0 to n] (i choose k) = (n+1 choose k+1). Sum [from i = 0 to n] (i^3) = (n^2)(n+1)^2 / 4 = (sum[from...

I am interested in knowing under what conditions the Euler-Maclaurin summation formula converges (including the remainder term). Is there anywhere in the texts or literature where they discuss this? Thanks.

If j^\mu = ( j^0 , \vec{j} ), why does \partial_\mu j^\mu = \partial_0 j^0 + \vec{\nabla} \cdot \vec{j} surely when you take a dot product of four vectors you get a subtraction as in a^\mu b_\mu = a^0 b_0 - \vec{a} \cdot \vec{b} Maybe I'm forgetting something

definition \{\vec{A},\vec{B}\}\cdot \vec{C}=\vec{A}(\vec{B}\cdot\vec{C}) \vec{C}\cdot \{\vec{A},\vec{B}\}=(\vec{C}\cdot\vec{A})\vec{B} I have a question. I found in some books that definition of tensor is \hat{T}=\{\vec{T}_k,\vec{e}_k\} where \hat{\T} is tensor! Is here...

How would I write the result of this in summation notation after multiplying it out? (\sum^{n}_{i=1} x_{i})^{2}

Homework Statement Evaluate: Sum[k2-k+1/k(k-1),{k,2,infinity}]Homework Equations The Attempt at a Solution k2-k+1/k(k-1) can be written as k/(k-1) - 1/k, but then I get stuck because when n->infinity, the sum is divergent.

How were they able to derive this?

can the lower bound of a summation(sigma) be any real number ? i.e ex: sigma(LB:sqrt(2) or (9/2) etc ) Even a lower bound be a real number is possible or not can upper bound be any real number or is it a strict rule that '1' should be added to lower bound to get the consecutive number.? i.e...

Homework Statement Evaluate: 1/4+2/16+3/64+4/256+5/1024+... Homework Equations The Attempt at a Solution The summation can be written as: Sum(k=1 to infinity, k/(4^k)) Then I do not know how to calculate the sum. Please help!

So what's going on here? Since there is a 2^(k-1), I can subtract one from n and also the index? Thats what it looks like they did. Also, where did they get that 1/2 from?

Ignore the above, I was haveing problems with the symbol... Convert each to closed form: 1. Sum from i=1 to n of: \frac{n}{a^n} 2. Sum from i=1 to n of: \frac{1}{a^n} Thanks. P.S. I know how to do it if it was an infinite series, but not for this.

Not exactly sure how they went from the first step to the 2nd step? Is there an easier way to solve this? (keep in mind we're dealing with floor and ceiling functions)

Homework Statement "A notation that you may find helpful in this task is the factorial notation n!, defined by n!=n(n-1)(n-2)….3 x 1 x 1 e.g. n!=5 x 4 x 3 x 2 x 1(=120) Note that 0!=1 Consider the following sequence of terms where x = 1 and a = 2. 1, ((ln2))/1, ((ln2)^2 )/(2 x 1)...

I'm trying to get a closed form of a summation, however n is in the summation itself. Here's an example: Ive never encountered such a thing. What happens to the n? Does it stay in there as n in the closed form? So then we have n/2^k which the closed form turns out to be: n/ [2^(n+1)-1...

I'm having a hard time understanding what this question is even asking for. Do I just write this summation in closed form? What does it mean by its last term, or the k=n term? I know I'm supposed to have at least attempted the problem, but I honestly have no idea what this question is even...

So here are my steps, which for some reason I feel are very wrong: Well in closed form would be [n(n+1)]/2 so 2k would be 2*[n(n+1)]/2 For 1.7^k, I used a different form, which I don't have the formula for in front of me, but the final result for that part is [1.7^(n+1) - 1] /[1.7 - 1] So...

Hello all, I have been thinking about a particular mathematical question (that I've made up) and I haven't been able to reach a solution yet.. I want to find the rule for the function F(x,y) which gives the number of different "ways" that the integer x can be expressed as the summation of...

Homework Statement I have this nasty summation and I am close to finding a way to calculate it with my graphing calculator. I just need to iron out the details. If I can rewrite the summation on terms of \bar{x}, \bar{y} and \sum x_iy_i I will be all set. I will explain these terms in a...

From the attachment. i would like to know how to find (t_1 and t_2)minimum if given t_0=0 and t_3=5.It seem like when using excel solver to find the minimum.anyone know how to do it with mathematica?

Homework Statement I am having trouble reading this notation \sum (i/k) The sum is from i=0 to n I wasn't sure how to write the combination of i,k on the computer so I just wrote it as i/k. Homework Equations When I say combination I am talking about this formula...

I am trying to Sum the total from the following equation B(t)=a * b^t So I have \sum a * b^t with t=1 to 321 Trying to solve for an equation and getting a(b^(t+1) - 1) / (b-1) Answer is not correct...help

Are the following three equivalent? P_{\alpha}A^{\beta}\tilde{\omega}^{\beta}(\vec{e_{\beta}} ) = \sum_{\alpha = 0}^{3}{P_{\alpha}\tilde{\omega}^{\alpha}(\sum_{\beta = 0}^{3}{A^{\beta}\vec{e}_{\beta}) = \sum_{\alpha = 0}^{3}{P_{\alpha}A^{\alpha}

Hi, So this is just part of my problem but its got me stumped for days and I can't ignore it since its popping up too often in my problems. Homework Statement For A sample of 140 bags of flour. The masses of x grams of the contents are summarized by \sum (x - 500) = -266 and \sum...

Homework Statement a) Show that $\sum_{S(j)} a_j + \sum_{R(j)} a_j = \sum_{S(j) and R(j)} a_j + \sum_{S(j) or R(j)} a_j$ is valid for an arbitrary infinite series, provided that 3 out of 4 sums exist. b) Show that $\sum_{R(j)} a_j = \sum_{R(c-j)} a_{c-j} for an arbitrary infinite series where...

Homework Statement Write the necessary equation of the object shown in Figure P8.4. Take the origin of the torque equation about an axis perpendicular to the page through the point O. (Let counterclockwise torque be positive and let forces to the right and up be positive. Use q for θ and Rx...

Homework Statement Using summation by parts, find Sum[n/3^n]. Homework Equations Sum[a_k*b_k] = s_n*b_(n+1) - Sum[s_k(b_(k+1)-b_k] The Attempt at a Solution Let a_k = 1/3^k and b_k = k. Then b_(k+1)-b_k = 1. But what is s_k? I know that it is 1/3 + 1/3^2 + 1/3^3 + ... but...

Homework Statement [PLAIN]http://www.hot.ee/jaaniussikesed/valem_kovar_erlt.bmp The first half of the equation is okay, but, after the second equal sign I started to improvise, did I mess up or is it correct? Trying to understand the indexes. ds being the differentially small distance...

Hi there I have read that the area of a peak can be approximated by summing the recorded peak intensities. I can't see how this works? If you add all the peak intensities together is not just the magnitude of their sum and not the area of the surface the peak overlays? Someone told me that...

Hi, We know that the Gaussian integral is \int_{-\infty}^{+\infty}e^{-\frac{x^2}{a^2}}dx=a\sqrt{\pi} However, if the gaussian function is discrete in x, what is the result of \sum_{n=0}^{+\infty}e^{-\frac{n^2}{a}} = \\? where n is natural number, that is n=0,1,2,3....

Homework Statement How do i evaluate the following sum \sum_{i=1}^{50}\frac{1}{(100-i)^{1/2}} Homework Equations The Attempt at a Solution i haven't a clue on how to do this, can someone please give me a hint? thank you

Homework Statement So, on a Fourier Series problem I came up with 2/3 + (8/π2)∑(1/n2)(-1)ncos(nπx/2) I'm supposed to Plot sm(x) versus x for m= 5, 10, 20 (m is the index of the summation, which starts at m=1) Homework Equations meh The Attempt at a Solution The...

\sum_{n=0}^{\infty} \frac{2^{n+1}(n+1)t^n}{(n+2)!}=\sum_{n=0}^{\infty} \frac{2^{n}nt^{n-1}}{(n+1)!} How are the above summation equal?

Does anybody help me how to find the average (expectation) of terms involving double summation? Here is the equation which I'm trying solve. [\tex]E\Big[2\sum_{k=0}^{N-2}\sum_{j=k+1}^{N-1}f(k,j)\cos[2\pi(j-k)t-\theta_{k,j}]\Big][\tex] where f(k,j) and [\tex]\theta_{k,j}[\tex] are some...

Homework Statement Let p(z) = \sum_{j=0}^{n} a_{n-j}z^j be a polynomial of at least degree 1 thus n \geq 1. Show that if z\neq 0 then 1/z is a root of the polynomial p. Homework Equations Fundamental theorem of Algebra The Attempt at a Solution If a expand the polynomial...

Homework Statement How can i prove this relationship \sum _{i=0}^k \text{Binomial}[n+1,k-2i] - \sum _{i=0}^k \text{Binomial}[n,k-2i]=\sum _{i=0}^k \text{Binomial}[n,k-1-2i] Homework Equations Binomial (n,k)=n^k/k! The Attempt at a Solution I attempted subbing into mathyematica but this didn't...