Summation Definition and 610 Threads

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..

(1/2) + (2/4) + ... + (n/(2^n)) = sum i=1 to i=infinity of (i/(2^i))?i know how to express the sum of just 1/(2^i), but not the above thanks for the help!

When needed to do that, I found it much easier to pretend it's an integral summation and then draw the area diagram then work it out from the picture the new terminals for the integral. Then convert that back into the discrete sum. Is that how you would do it? However for three or more...

Given nonzero whole numbers n, prove 13+23+33+...+n3=(1+2+...n)2 I figured this out numerically, but lack the skills to solve it analytically (no doubt by induction) and could not find it in my table of summations. I'm too old for this to be homework.

Can someone help me break this down? \Sigma^{k}_{i=1}\frac{i \left(^{n}_{i}\right)\left(^{m}_{k-i}\right)}{\left(^{m+n}_{k}\right)}

I was looking at the web page containing a derivation for the Poisson distribution: http://en.wikipedia.org/wiki/Poisson_distribution which derives it as the limiting case of the binomial distribution. There is a simplification step which I am missing, which is the step(s) between...

Im not sure if it is related to calculus but, Calculate the sum \sum^{\infty}_{n=0}\frac{(n-1)(n+1)}{n!} exactly. I tried to to partial fraction decomposition but couldn't find anything.

I have the summation x(1/2)^x for (x=1,2,3,4,...) So I set it up as s=1(1/2)+2(1/4)+3(1/8)+4(1/16)... This is however where I'm lost, I'm not exactly sure how to sum an infinite sequence, it hasn't really been introduced in any of my math courses, it just popped up in a statistics problem...

Getting E[N] from the multinomial dist, where \frac{n!}{n_{1}!n_{2}!... n_{r}!}p^{n_{1}}_{1}}p^{n_{2}}_{2} ... p^{n_{r}}_{r} is the pmf. Does this look right? \Sigma^{n}_{i=1}E\left[e^\left\{{\Sigma^{r}_{k=1}t_{k}N_{k}}\right\}}\right]...

Has anyone heard about a way to find the sum of a serie of this form: s=\sum_i{\exp(a+b\sqrt(i))}

[SOLVED] Summation Notation - Variable in the exponent Homework Statement This is an example formula. How do I solve a summation if something is in the form of Sum(c^i), where c is some constant?

[SOLVED] Summation - Riemann Intergral - URGENT Homework Statement Im working on the upper and lower riemann sums of f(x) = exp(-x) where Pn donates the partition of [0,1] into n subintervals of equal length (so that Pn = {0,1/n,2/n,...,1}) Homework Equations The Attempt at...

I'm having trouble picking apart this summation: \sum^{inf}_{n=1} P(E)*P(1-p)^{n-1}; where p = P(E) + P(F) I know I need to use the identity of a geometrical series when |r| < 1 : 1/(1-r) I'm getting P(E)/(1-(P(E)+P(F)) But I need to be getting P(E)/((P(E)+P(F)); The entire...

Homework Statement I am looking for a closed form of the summation: sin(x) + sin(3x) + sin(5x) + ... + sin((2n-1*)x) Homework Equations None. The Attempt at a Solution Through a complete stroke of luck, I believe I have arrived at the correct solution: sin^2(nx)/sin(x) I have...

[SOLVED] radius of convergence of an infinite summation Homework Statement find the radius of convergence of the series: \sum\frac{(-1)^k}{k^2 3^k}(z-\frac{1}{2})^{2k} Homework Equations the radius of convergence of a power series is given by \rho=\frac{1}{limsup |c_k|^{1/k}}...