Sums Definition and 370 Threads

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...

Homework Statement Not sure this is the right forum to ask a question regarding F-statistics, but please help if you are familiar with this stuff. The first part of homework was to prove mathematically that if a model has k variables, then F-statistic for testing model significance is...

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...

I have a homework question that reads: Represent the following rational functions as sums of elementary fractions and find the primitive functions ( indefinite integrals ); (a) f(z)=z-2/z^2+1 But my confusion arrises when I read sums of elementary fractions. I think what the question is...

So I'm taking an introductory number theory course as an undergraduate, and this particular "genre" of questions really just has me stumped. Pick a prime p such that p is odd. Now, take various sums up of natural numbers from 1 to p, and show that the results are divisible by p. For...

hi i m hashim i want to solve a qquestion 1.if x is rational & y is irrational proof x+y is irrational? 2. if x not equal to zero...y irrational proof x\y is irrational?? 3.if x,y is irrational ..dose it implise to x+y is irrational or x*y is irrational thanks please hashim

I was trying to build a probability-related software package and needed to have a theoretical framework to deal with some less common issues (i.e. stuff that you don't find in the average textbook). I was hoping that somebody could give me pointers as to where to find the proper formulae...

Cantor set defined via sums, whaaaaa?!? problem 19 chapter 3 of Rudin. I'm totally lost, I've even done a project on the Cantor set before but I just don't know where to start here. Associate to each sequence a=(p_n) in which p_n is either 0 or 2, the real number x(a) = sum from 1 to...

Howdy everyone. I'm not very good at writing proofs, so I am wondering if someone can tell me if I'm even on the right page with this. I am not sure if I understand the idea correctly. The theorem goes as follows: Suppose V is a finite dim. vector space with subspaces U and W such that V is the...

Hello I'm having some difficulty in finding sums which relate to Riemann integrals. The first one seems pretty simple.. a finite calculation of what would otherwise be the harmonic series i.e. 1/k from k=n to k=(2n-1). I can't see an easy way of finding a formula in terms of n, however...

Homework Statement The following sum \sqrt{9 - \left(\frac{3}{n}\right)^2} \cdot \frac{3}{n} + \sqrt{9 - \left(\frac{6}{n}\right)^2} \cdot \frac{3}{n} + \ldots + \sqrt{9 - \left(\frac{3 n}{n}\right)^2} \cdot \frac{3}{n} is a right Riemann sum for the definite integral. Solve as n->infinity...

Homework Statement The sum of two numbers is 20. What is the least possible sum of their squares. 2. The attempt at a solution Before I show my work, I'm pretty sure I have the answer. I think it's 200. If you add 10 and 10, you will have 20. If you square 10 you get 100, thus the sum...

Hi guys, I'm working on a project at the moment where I want to convert a sum to an integral but I am out of ideas. Basically I have something like: Sum over h: [f(h+0.5dh)]^(-1) - [f(h-0.5dh)]^(-1) where h goes from 0 to H. Any tips would be appreciated!

Use the riemann sums model to estimate the area under the curve f(x) = x^2, between x =2 and x = 10, using an infinite number of strips. Be sure to include appropriate diagriams and full explanation of the method of obtaining all numerical values, full working and justification. Does anybody...

Here is the question from the book: ------ Let n\geq1 and let a_1,...,a_n and b_1,...,b_n be real numbers. Verify the identity: \left(\sum_{i=1}^n{a_ib_i}\right)^2 + \frac{1}{2}\sum_{i=1}^n{\sum_{j=1}^n{\left(a_ib_j-a_jb_i\right)^2}} =...

I do have a series of channels that contain the number of radioactive counts within a small energy range. Since the occurence of radioactive decay is statistical, the error in the number of counts is simply the square of the number of counts. Each channel contains counts from two different...

Homework Statement The voltage across a resistor is given by: v(t) = 5 + 3 \cos{(t + 10^o)} + \cos{(2 t + 30^o)} V Find the RMS value of the voltage Homework Equations For a periodic function, f(t), the rms value is given by: f_{rms} (t) = \sqrt{\frac{1}{T} \int_{0}^{T} f(t)^2 dt} Where T...

I don't think I *really* understand the Central Limit Theorem. Suppose we have a set of n independent random variables \{X_i\} with the same distribution function, same finite mean, and same finite variance. Suppose we form the sum S_n = \sum_{i=1}^n X_i. Suppose I want to know the...

Is there ever a situation where it is more appropriate/advantageous to use Riemann summation as opposed to evaluating an integral, or is Riemann summation merely taught in order to help the student to understand what's going on?

Hello everyone I'm studying for my next exam and I screwed up on the geometric progressions and arthm and they are the easiest of them all but I don't know what I'm doing wrong. The first problem on the exam said: Suppose that an arithmetic series has 202 terms. If the first term is 4PI and...

Hello everyone, I was wondering if someone can double check my work for #'s 25 and 31. The directions say: Express each of the sums in closed form (without using a summation symbol and without using an ellipis...).http://img224.imageshack.us/img224/3514/lastscanle2.jpg Thanks!

I have just made the following variable switch: \sum_{i=0}^n\sum_{j=0}^m\binom{n}{i}\binom{m}{ j}x^{i+j}=\sum_{k=0}^{n+m}\sum_{i=0}^k\binom{n}{i}\binom{m}{k-i}x^{k} I know it's right, but is there a method I can use to prove without a shadow of a doubt that it is?

Let A(n) = {1,2,3,4, … 8} and B(n) = {1,2,3,4, …. 16} be two sets of consecutive integers with no repetition. Divide the set of elements B(n) into two subsets C(n) and D(n) each comprising 8 different integers and such that every element of B(n) is used with the condition that 8 equations...

Can someone confirm/disprove the following: If X\subset\mathbb{P} is infinite, then \sum_{n\in X}\frac{1}{n} diverges or is irrational.

Some sums, don't sum up :) I have a problem that require some math tricks, and after I tried to solve it myself I looked at the answer and I don't understand how this is done : \[ \sum\limits_{k = 0}^n {\left( {\frac{2}{5}} \right)^k } + \sum\limits_{k = 0}^n {\left( {\frac{3}{5}}...

Which squares are expressible as the sum of two squares? Is there a simple expression I can write down that will give me all of them? Some of them? Parametrization of the pythagorean triples doesn't seem to help.

1) develop the function f(x)=(e^x)sin(x) into a power sum over the point 0. 2) find the convergence radius R of \sum_{\substack{0<=n<\infty}}\frac{(n!)^2}{(2n)!}x^n and say if it converges or diverges at x=-R, x=R. about the second question i got that R=4, through hadamard test, but i didnt...

I have a problem I'm working on where the general premise is that there is a box being pushed along the ceiling at a constant speed. The force F is at some angle with respect to the vertical. There is a coefficient of kinetic friction between the box and the ceiling and the persons hands and the...

Which command in Mathematica will give me the sum of the digits of a number in base 10? Thanks.

"strange" sums... Let be the next 2 sums in the form: f(x)+f(x+1)+f(x+2)+... (1) and f(x)+f(2x)+f(3x)+... (2) how would you calculate them?..well i used a "non-rigorous" but i think correct method to derive their sums..let be the infinitesimal generator D=d/dx...

I am doing exactly what this article is saying in order to try to graph a sequence of partial sums. If I enter the syntax, given below, on the home screen, it will list the first 25 terms of the partial sum. How do I graph those terms using sequence mode...

Hi, I just need a little help in getting some sums. Can anyone of you give me a site where I can find sums in Log so that I can do them and practice a lot. I mean like sums in this type Show that log(xy)base16 = 1/2log(X)base4 + 1/2log(Y)base4 Thanks just need some sums of this type...

I need to calculate \sum_{i=1}^n \frac{1}{i(i+1)} useing the fact that: \sum_{i=1}^n F(i) - F(i-1) = F(n) - F(0) now I chose the function F(i) = \frac{1}{i} \frac{1}{(i+1)} ... \frac{1}{(i+r)} so F(i)-F(i-1)=(\frac{1}{i}\frac{1}{(i+1)} ...

This discussion is that of converting infinite series to infinite products and vice-versa in hopes of, say, ending the shortage of infinite product tables. Suppose the given series is \sum_{k=0}^{\infty} a_k Let S_n[/tex] denote the nth partial sum, viz. S_n=\sum_{k=0}^{n} a_k so...

In an equation, the upper sum is Mi = 0+i(2/n) and the lower sum is mi = 0+(i-1)(2/n) So the question is why is it (i-1) for the lower sum and only i for the upper sum? Any help is highly appreciated! ^_^