Sums Definition and 370 Threads

using an exponential regulator exp(-\epsilon n) the sum 1+2+3+4+5+6+7+...= -1/12+ 1/\epsilon^{2} and for Casimir effect 1+8+27+64+125+...= -1/120+ 1/\epsilon^{4} can i simply remove in the calculations of divergent series 1+2+3+4+5.. and similar the epsilon terms imposing...

Homework Statement If f:(-a,a)-->Real numbers, then f can be rewritten as the sums of an even and an odd function Let k: Real numbers\{-1}-->Real numbers be given by k(x)=\frac{x^2+4}{x+1} (i) Prove that there is no interval (-a,a) on which k is either even or odd (ii) Find an even...

Homework Statement If b>a, find the infimum of b - a for arbritrary b,a. Homework Equations - The Attempt at a Solution So this is for a darboux sum but I'm stuck on proving that 0 is the inf. It seems really easy but I can't seem to think straight. First thing is 0 is a lower...

I've been trying to tackle a problem of the following form lim_{n \rightarrow \infty} \sum_{k=0}^n f(k,x) I know that the limit of each function is zero as n goes to infinity. ie. lim_{n \rightarrow \infty} f(n,x) =0 But I'm not sure how to approach the problem above. I would greatly...

I'm stuck on how to approach the following problem. lim_{x \rightarrow \infty} \sum_{j=0} ^x e^{-j/x} Does anyone have any ideas?

Given linear transformations S: Rn --> Rm and T: Rn --> Rm, show the following: a) S+T is a linear transformation b) cS is a linear transformation I know that since both S and T are linear transformations on their own, they satisfy the properties for being a linear transformation, which is that...

Homework Statement FIND THE LOWER SUM FOR THE REGION BOUNDED BY f(x) = 25 - x^2 AND THE X - AXIS BETWEEN x = 0 and x = 5. SOLVE ANALYTICALLY! Homework Equations None that I'm aware of... The Attempt at a Solution f(x) = -x2 + 25 and \DeltaX = b-a/n = 5-0/n = 5/n Here's...

Homework Statement Prove that the integral from 0 to x of (sin t)/(t + 1) dt > 0. (Sorry I don't know how to use the integral latex.)Homework Equations We have only learned about lower and upper sums, and how the integral is equal to the supremum of lower sums and the infimum of upper sums when...

Homework Statement This is somewhat a repost... except I have figured out some of it and I have cleaned up the question. Your task is to estimate how far an object traveled during the time interval 0<= t >= 8 , but you only have the following data about the velocity of the object...

Homework Statement I really need help starting this problem as I am not sure what to do. Your task is to estimate how far an object traveled during the time interval 0t8 , but you only have the following data about the velocity of the object. time (sec) 0 1 2 3 4 5 6 7 8...

Homework Statement The following table shows the power produced by a 600kW wind turbine at the given wind speed and the number of hours the wind blows at that speed. a) Plot the power characteristic as a function of wind speed. b) Plot the wind duration curve as a function of wind speed...

Hi there! Here are a few sums that are making me go nuts:cry:( actually can't get any clue how to solve:confused:) so here they are ( a+x)^1/3 + (a-x)^1/3= b ( Gosh I wish there could be some rule so that we could straight away write a^ 1/3 and x^1/3 anyway:-p) And 1/p+q+x=1/p+1/q+1/x I...

Homework Statement Let E and F be two subspaces of R^n. Prove the following statements: (n means "intersection") If EnF = {0}, {u1, u2, ..., uk} is a linearly independent set of vectors of E and {v1, v2,...vk} is a linearly independent set of vectors Note: Above zero denotes the...

I am looking for a Hoeffding-type result that bounds the tail of a sum of independent, but not identically distributed random variables. Let X_1,..,X_n be independent exponential random variables with rates k_1,...,k_n. (Note: X_i's are unbounded unlike the case considered by Hoeffding) Let S=...

http://img156.imageshack.us/i/17818455.jpg/ http://img215.imageshack.us/i/53355598.jpg/ http://img509.imageshack.us/i/11493310.jpg/ If you look at the above, I have underlined the problem that I am having. So, my first question is, where are these inequalities coming from? If you do have...

Homework Statement Homework Equations The Attempt at a Solution I have attachments that can answer the above template, and please look at the attachments if you are trying to help me. I have two questions regarding upper and lower sums & Riemann sums. So, the attachments 1 & 2 are...

Homework Statement Not an actual problem, but to help solve my homework, would cos(A+B+C)= CosACosBCosC-SinASinBSinC (Cos(x+y)=cosxcoxy-sinxsiny) I was unsure if this can be applied to multiple digits or only 2. I know I could plug in numbers to test, but I was wondering about...

Homework Statement Give an example of a sequence (a_n) so that lim_{n\rightarrow\infty} \left|a_{n+1}/a_{n}\right| =1 and \sum^{\infty}_{n=1} a_{n} convergesHomework Equations (Maybe relevant, maybe not) Theorem which states: If \sum^{\infty}_{n=1} a_{n} converges, then...

If U_1, U_2, U_3, are subspaces of V (over fields R and/or C), is the addition of the subspaces commutative and associative? To me it seems rather trivial .. Since their summation is simply the set of all possible sums of the elements of U_1, U_2, U_3, and the elements themselves are...

Homework Statement Let X be the height of a man and Y be the height of his daughter(both in inches). Suppose that the joint probability density function of X and Y is bivariatenormal with the following parameters: mean of X=71, mean of Y=60, std. deviation of X=3, Std. deviation of Y=2.7...

Homework Statement Vicki owns two separtment stores. Delinquent charge accounts at store #1 show a normal distribution, with mean $90 and std. deviation $30, whereas at store #2, they show a normal distribution with mean $100 and std. deviation $50. If 10 delinquent accounts are selected...

Homework Statement The distribution of the IQ of a randomly selected student from a certain college is N(110,16). What is the probability that the average of the IQ's of 10 randomly selected students from this college is at least 112? Homework Equations I think we need P(Sample Mean...

Homework Statement Suppose X1 , X2 , X3 , and X4 are independent with a common mean 1 and common variance 2. Compute Cov( X1 + X2 , X2 + X3). Homework Equations Cov (X,Y) = E[(X-u)(Y-v)] = E[XY] - uv, where u and v are the means of X and Y E[XY] = E[X]E[Y] E[X+Y] = E[X] + E[Y] The Attempt...

I have a rudimentary understanding of integration as it applies to finding the area under a curve. I get the idea of adding up the areas of progressively smaller rectangles to approach the area, and that at an infinite number of rectangles the areas would be exactly the same. Right now I'm just...

Homework Statement Hi and thank you for reading this! Let \left.f(x) = cos(x) + cos\left(\pi x\right) a) show that the equation f(x)=2 has a unique solution. b) conclude from part a that f is not periodic. Does this contradict withe the previous exercise that states if...

I am actually attempting the proof for Minkowski's inequality, but have not gotten that far yet. I am stuck on a step in Holder's inequality, and I have a feeling it's something very simple that I am just overlooking... I have easily been able to show ab \leq \frac{a^p}{p} + \frac{b^q}{q}...

Homework Statement Express the integral as a limit of sums. Use right endpoints. Do not evaluate the limit. \intsin(x^{4}dx from 0 to 6 Homework Equations \sumf(xi)\Deltax The Attempt at a Solution What I'm unsure of here is what exactly the question is asking. How far do I go...

"Of the numbers N>1, only 4 and 6 cannot be expressed as a sum of prime numbers with unique values."

[b]1. Use Taylor's expansion about zero to find approximations as follows. You need not compute explicitly the finite sums. (a) sin(1) to within 10^-12; (b) e to within 10^-18: [b]3. I know that the taylor expansion for e is e=\sum_{n=1}^{\infty}\frac{1}x^{n}/n! and I aslo know that...

Sequences, Cumulative Sums, Partial Sums Plot --- Ti-89 Titanium My proffessor just gave us all these packets for all these programs he wants us to put into our calculators. They are for a Partial Sums Plot, and a List of Cumulative Sums, nth terms and differences. They're all for the Ti-83...

Homework Statement Let {x_n} be a sequence. and let r be a real number 0<r<1. Suppose |x_(n+1) - x_n|<=r|x_n -x_(n-1)| for all n>1. Prove that {x_n} is Cauchy and hence convergent. Homework Equations if |r|<1 then the sequence \sum r^k from k=0 to n converges to 1/(1-r) The...

Homework Statement How to find the Sn of this patial sum : 1/n+3 - 1/ n+1 ?? Homework Equations Finding the terms The Attempt at a Solution In fact, I tried finding s1 and s2 and so on till s6 and I found that the Sn is -1/ n+2 after I canceled the terms, is that right ??

at the very end of this lecture http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM10.pdf and the very beginning of this lecture http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM11.pdf we look at evaluating this sum by making it into an integral by two...

Decide (with justification) if the following series converges or diverges; Sum(1,infinty) (2^(n)+3^(n))/(4^(n)+5^(n)) I've tried using the ratio test but I couldn't see that it was helping in any way, should I be using a different type of test for this problem? I really can't see where to...

Homework Statement Let U and W be subspaces of V. What are U+U, U+V? Is U+W=W+U? Homework Equations The Attempt at a Solution It is easy to show that U+U and U+V are spaces too under closed addition and scalar multiplication, but I'm not sure where they lie. For example, is U+U a...

I understand that the limit of the sum of two sequences equals the sum of the sequences' limis: \displaysyle \lim_{n\rightarrow\infty} (a_{n} + b_{n}) = \lim_{n\rightarrow\infty}a_{n} + \lim_{n\rightarrow\infty}b_{n}. Similar results consequenly hold for sums of three sequences, four sequences...

Homework Statement Prove that \displaystyle\sum_{x=2}^n \frac{1}{x^2}<\int_0^n \frac{1}{x^2} dx Homework Equations I'm not sure what equations are relevant for this, but I think for this I would need: \displaystyle\sum_{x}^{\infty} \frac{1}{x^s} =...

Homework Statement I am a first-year physics student learning calculus. my question is about the approximation of the area of a region bounded by y = 0. Homework Equations Use rectangles (four of them) to approximate the area of the region bounded by y = 5/x (already did this one), and y =...

Homework Statement I am given a left riemann sum program module in Mathematica and need to convert it into the right riemann sum. The program takes values for x and f/x and the partition and graphs on a certain interval provided. leftRiemannGraph[f_, a_, b_, n_] := Module[{expr}, expr[1]...

Homework Statement Hi all. Lets assume that we know the following: \sum\limits_{n = - \infty }^\infty {\varepsilon _n (t)} \exp ( - i\omega _n t) = a_0 + \sum\limits_{n = 1}^\infty {\varepsilon _n (t)} \exp ( - i\omega _n t), where a0 is the contribution for n=0. Now I have an...

Hi, Can anyone derive the sum of exponentially distributed random variables? I have the derivation, but I'm confused about a number of steps in the derivation. Here they are: Random variable x has the PDF, f(s) = \left\{ \begin{array}{c l} e^{-s} & if s \ge 0 \\ 0 &...

Need some urgent help with Riemann Sums. Homework Statement PART A: In all of this question, let I = \int ^{2}_{-2} f(x)dx where f(x) = -2x + 1 Evaluate I. PART B: Use the defintion of the definite integral to evaluate I. i.e Riemann Sum. Homework Equations The...

Homework Statement Express the integral as a limit of Riemann sums. Do not evaluate the limit. Homework Equations \int_0^{2\pi} x^{2}sin(x)\,dx The Attempt at a Solution I really don't know where to start...any help getting me started would be highly appreciated!

let be the exponential sum S= \sum_{n=1}^{N}e( \frac{f(x)}{p}) e(x)= exp( 2i \pi x) my conjecture is that since the complex exponential takes its maximum value '1' when x is equal to an integer then Re(S)= \Pi (f,N) with \Pi (f,N) is the number of solutions on the interval...

Homework Statement Find the limit, as n -> infinity, of \sum_{k=1}^nk3/n4 Homework Equations Riemann sum: S(f, \pi, \sigma) = \sum_{k=1}^nf(\xi)(xk - xk-1) The Attempt at a Solution My guess is that I should try to put this sum in terms of a Riemann sum, and then taking n -> infinity will...

Homework Statement sin²(1°)+sin²(3°)+sin²(5°)+...sin²(359°)= ? And : 1!+2!+3!+4!+...+2006!, asked are he last two numbers of this sum. Homework Equations I don't know anyThe Attempt at a Solution I don't know how to calculate Sin with your head, and 2006! is way to hard to calculate. Is...

Is it possible to represent the dot product (matrix multiplication) with sums? For example, know the dot product of a polynomial and another one [i.e. 2+5x and 3x+7x2] would be the sums of the products. [i.e. 2(3x) + 5x(7x2)]. Could this be also written as \sum^{n}_{i=1} a1ibi1? I'm asking...

http://www.youtube.com/watch?v=mg5tl87rEE4&eurl= This video need to be distributed in newpapers in swing states instead of this crap: http://www.npr.org/templates/story/story.php?storyId=95076174

Homework Statement Show (without proof) : For every k, there exists a arbitrarily large n that are not the sum of k fibbonacci numbers. The Attempt at a SolutionReally i am pretty lost here. I tried to do a proof by induction, but this didnt work. Then i realized i am not supposed to do a...

Alright, I started doing Riemann sums and I am ripping my hair out in frustration. I just can't wrap my head around how I'm supposed to do it, and my woefully vague textbook isn't helping either. I'm wondering how I'm supposed to solve a Riemann sum question with sigma notation (no limits), and...