Sums Definition and 349 Threads

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 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 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...

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...

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...

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...

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...

HI guys, i was wondering whether there is any site online where i could read about darbu sums. Because i want then to define the definite integral using darbu sums. I had a book, written by a russian mathematician, but i forgott it home, so there is no way i can get hold of it. So, any...

The sum of two subspaces seems a simple enough concept to me, but I must be misunderstanding it since I don't understand why Axler gives an answer he does in Linear Algebra Done Right. Suppose U and W are subspaces of some vector space V. U = \{(x, 0, 0) \in \textbf{F}^3 : x \in...

Could anyone provide me with a proof for Newton's Sums? So far, I've gotten as far as showing for a polynomial P(x)=anxn+an-1xn-1+...+a1x+a0 with roots x1, x2,..., xn that P(x1)+P(x2)+P(x3)+...+P(xn)=0 and so, anSn+an-1Sn-1+...+a1S1+na0=0 and...

This is from a final exam on the MIT Open Course Ware site for Single Variable Calculus Homework Statement (a)(5 points) Write down the general formula for the Riemann sum approximating the Riemann integral, 1 \int f(x)dx 0 for the partition of [0,1] into n subintervals of equal...

I'd like to see whether weird reciprocal sums of integers in the form \sum_{x\in S}\frac{1}{x}, where S is some unconventional set of integers, converges or diverge. Does anyone know any? For example, \sum_{x\in S}\frac{1}{x} where S is the set of integers that, when expanded in binary...

The question is: Rolling a sum of 8 and a sum of 6 BEFORE rolling two sums of 7 Experimental Probability: 55% Theoretical Probability: 54.5% How did they do this? I understand that to get a sum of 8: 13.888% 6: 13.888% 7: 16.666% 6/8: 27.777% but I don't understand how they figured...

Homework Statement Prove that \sum_{k=0}^{l} \binom{n}{k} \binom{m}{l-k} = \binom{n+m}{l} Homework Equations If a and b are any numbers and n is a natural number, then (a+b)^{n}=\sum_{j=0}^{n} \binom{n}{j} a^{n-j}b^{j} The Attempt at a Solution I know that...

[SOLVED] Linear Algebra - Direct Sums Homework Statement Let W1, W2, K1, K2,..., Kp, M1, M2,..., Mq be subspaces of a vector space V such that W1 = K1 \oplusK2\oplus ... \oplusKp and W2 = M1 \oplusM2 \oplus...\oplusMq Prove that if W1 \capW2 = {0}, then W1 + W2 = W1 \oplusW2 = K1...

This is a general question, I guess. If I am given an infinite series, how do I go about finding its sum using Fourier expansion?

Homework Statement Prove that the following sums only converge at 0. sum of: e^(n^2)*x^n , and sum of: e*n^(n)*x^(n) Homework Equations well i know series converge if the lim as n approaches inf of the abs(x-c) is less than (An/An+1) but I have no idea how to prove it, I saw these for...

Does anyone know if there is a way to divide up the area of a circle using similar polygons, with a common ratio? I was just curious if there is a way, or if it has been proven impossible. For example, I tried inscribing a square inside a circle and making an infinite series of triangles with...

\sqrt{2+\sqrt{3}}+\sqrt{4-\sqrt{7}}=\sqrt{5+\sqrt{21}}

Hi, I'm trying to figure out my TI-89. So I want to estimate the 40th partial sum of this series: Sum(40) of (-1^(k+1))/k^4, starting at k=1. My major problem is that I want to use 'k's or 'n's, not 'x's. Is there a difference? I haven't asked my Calc teacher about this yet, but I know that...

Homework Statement Using the macluarin's expansion for sinx show that \int sinx dx=-cosx+cHomework Equations sinx=\sum_{n=0} ^\infty \frac{(-1)^nx^{2n+1}}{(2n+1)!} The Attempt at a Solution Well I can easily write out some of the series and just show that it is equal to -cosx but if I...

Please HELP...Don't Understand Simple Concept on Riemann Sums Can someone please explain this to me... The number of subintervals in a partition approaches infinity as the norm of the partition approaches 0. That is, ||Triangle|| approaches 0 implies that n approaches infinity. I thought...

Please help! Struggling with finding the area using upper & lower sums! I can't load the picture on here so I will explain it the best I can... It is the graph of 1/x and there are 5 subintervals starting at x = 1 and ending at x = 2. It says to use upper and lower sums to approximate the...

I often see people use the Riemann definition of the integral to solve a certain limit-series computation, but they usually just skip a step that I can follow one way but not the other. Given the integral, I can see the limit-series that comes from it, but when trying to find the integral from...