Sum Definition and 1000 Threads

Hi! I want to write a program in c, that calculates the sum [1+sum{1/(i(i+1)) from 1 to n}]. I declared the variables as float. When I run the program with n=9, the output is 1.899999976, but when I calculate this with a calculator the result is 1.9. Where is the error?

Obtain the probability of getting a sum of 13, when four fair dice are rolled together once. if we do by just calculating all possible values of sum,then it will take more time. so,we can do above problem as Multinomial Coefficents of sum i.e.,x1+x2+x3+x4 = 13 where,1<= xi <= 6,for all 1<= i <=...

A set A of non-zero integers is called sum-free if for all choices of a,b\in A, a+b is not contained in A. The Challenge: Find a constant c > 0 such that for every finite set of integers B not containing 0, there is a subset A of B such that A is sum-free and |A| ≥ c|B|, where |A| means the...

I am reading the paper on the Casimir effect and they measure the space in between the plates using a sum and the energy of the vacuum without the plates using an intregal. Why do they use the sum and intregal, should they be switched.

Hi everyone, :) I encountered this question and thought about it several hours. I am writing down my answer. I would greatly appreciate if somebody could find a fault in my answer or else confirm it is correct. :) Problem: Let \(V_1,\,\cdots,\,V_k\) be subspaces in a vector space \(V\)...

How would you Integrate a Sigma Sum?

I'm doing problem section 15 chapter 1 by Boas. I don't want to ask about a particular problem in there but she often gives this kind of instruction, "By computer or tables, find the exact sum of each of the following series." My question is, what kind of table she is referring to? I take it...

In a matrix the sum of element of a matrix in a row times it's co factor of that elemt gives the determinant value, but why does the sum of element of a matrix times cofactor of different row is always zero?

Hi MHB, This problem vexes me until my mind hurts. Problem: Find the sum of the first 11 terms of the series $$\frac{19}{99}+\frac{199}{999}+\frac{1999}{9999}+ \cdots$$ Attempt: I managed only to find the expression of the nth term of the given series and I got...

Homework Statement Let us choose at random a point from the interval (0,1) and let the random variable X_1 be equal to the number which corresponds to that point. Then choose a point at random from the interval (0,x_1), where x_1 is the experimental value of X_1; and let the random variable...

Homework Statement Prove Ʃ1/(n^2) as n goes to infinity = (∏^2)/8 Homework Equations The Attempt at a Solution No idea how to start. Pls guide. Thanks

Suppose that x\in H, where H is a Hilbert space. Then x has an orthogonal decomposition x = \sum_{i=0}^\infty x_i. I have a linear operator P (more specifically a projection operator), and I want to write: P(x) = \sum_{i=0}^\infty P(x_i). How can I justify taking the operator inside the...

Let $p$ be the sum and $q$ be the product of all real roots of the equation $x^4-x^3-1=0$. Prove that $q<-\dfrac{11}{10}$ and $p>\dfrac{6}{11}$.

Prove the following Euler sum $$\sum_{k\geq 1}\left(1+\frac{1}{3}+\cdots +\frac{1}{2k-1} \right) \frac{x^{2k}}{k}=\frac{1}{4}\ln^2\left( \frac{1+x}{1-x}\right)$$

Homework Statement f(t) a continuously differentiable function twice over the circle T1 cr its Fourier coefficients and σn(f,t) partial sum of Fejer. a.Demonstrate that http://imageshack.us/a/img94/5992/ds35.png b. Consider k as -n≤k≤n , using cr coefficients calculate...

I know there are many proofs for this but I am having trouble proving this fact using my book's definition. My book defines first a non negative measurable function f as a function that can be written as the limit of a non decreasing sequence of non-negative simple functions. Then my book...

Write out the minimal Sum of Products(SOP) equation given the following Karnaugh Map. YZ|WX 00 01 11 10 00 d 1 1 1 01 1 1 0 0 11 0 0 d 1 10 0 0 0 0 Need someone to check my answer. My answer: $$yzw + \bar{y}\bar{z} + \bar{y}\bar{w}$$

Hi, I am trying to make progress on the following integral I = \int_0^{2\pi} \sqrt{(1+\sum_{n=1}^N \alpha_n e^{-inx})(1+\sum_{n=1}^N \alpha_n^* e^{inx})} \ dx where * denotes complex conjugate and the Fourier coefficients \alpha_n are constant complex coefficients, and unspecified...

Homework Statement Let ##T\in L(V,V)## such that ##T^{2}=1##. Show that ##V=V_{+}\oplus V_{-}## where ##V_{+}=\{v\in V:T(v)=v\}## and ##V_{-}=\{v\in V:T(v)=-v\}##.The Attempt at a Solution I was given a theorem that said that ##V## is the direct sum if and only if every vector in ##V## can be...

It's a theoretical study. I would like to understand how the sum of forces can be at 0 if I put an object (vacuum in it) in a big liquid disk (disk is fulled with liquid), the disk is big enough for agglomerate liquid (like this works with a planet, matter is agglomarate with gravity). There is...

Show that $3^{2008}+4^{2009}$ can be written as product of two positive integers each of which is larger than $2009^{182}$

Homework Statement Three yearly losses. First: Exponential Second & Third: Weibull Losses are independent. Find the 95% VaR of the min loss Homework Equations The Attempt at a Solution My first thought was: Let L be total loss, A be first Loss, B be second loss, C be third...

Homework Statement suppose that the partial sum of the series (sigma)n=1,infinity an is given by the partial sum Sn = (-2n+9)/(-6n+15). Find an expression for an when n>1 Homework Equations Sn= (-2n+9)/(6n+15 The Attempt at a Solution So I attempted to subtract S(n-1) from S(n) to get each...

I found this on the internet, but did not find the proof. Curious to me is that the the ratio and root test have the same conditions. How can i basically prove this equality? $$\frac{a_{n+1}}{a_{n}} = \sqrt[n]{a_{n}}$$ Thank you!

Evaluate sum: $\displaystyle S=\sum_{k=0}^{2n}(-1)^k{2n\choose k}{4n\choose 2k}$

converge or diverge? $$\sum_{n=1}^{^{\infty }}a_{n} $$ $$a_{1}= \frac{1}{3}, a_{n+1}= \sqrt[n]{a_{n}} $$ Im having problems to solve this exercise, i would like to see your solutions

Simplify $$\frac{\sum\limits_{k=1}^{99}\sqrt{10+\sqrt{k}}}{ \sum\limits_{k=1}^{99}\sqrt{10-\sqrt{k}}}$$

Put $1\le n\in\mathbb Z$ Find the Sum: $S_n=\displaystyle \sum_{k=1}^n\dfrac{2k+1-n}{(k+1)^2(n-k)^2+1}$

Wolfram MathWorld states that $$ \sum_{n=1}^{\infty} \frac{1}{n^{3} \binom{2n}{n}} = \frac{ \pi \sqrt{3}}{18} \Big[ \psi_{1} \left(\frac{1}{3} \right) - \psi_{1} \left(\frac{2}{3} \right) \Big]- \frac{4}{3} \zeta(3) $$ where $\psi_{1}(x)$ is the trigamma function. But I can't get my answer in...

The Total Sum of $5$ Digit no. which can be formed with the Digit $0,0,1,1,2,2,3,3,4,4,4,5,6$ [a] without Repetition of Digit. [b] with Repetition of Digit

The Total Sum of $5$ Digit no. which can be formed with the Digit $0,1,2,3,4,5,6,7$. [a] when repetition of digit is allowed [b] when repetition of digit is not allowed

I have a sum \sum_{n=-\infty}^{\infty} f(n) which I do not want to consider the convergence of in the normal sense, but I want to talk about the limit \lim_{N\to \infty} \sum_{n=-N}^{N} f(n). I know that when this limit exists the sum is _____ convergent, or is a _____ sum, where _____ is...

Please compute the following sum: $$S_n=\sum_{k=1}^{n}\frac{n!}{(k-1)!(n-k)!}$$

Is the following statement true? I am trying to see if I can use it as a lemma for a larger proof: Let ##V## be a vector space and let ##W, W_{1},W_{2}...W_{k} ## be subspaces of ##V##. Suppose that ## W_{1} \bigoplus W_{2} \bigoplus ... \bigoplus W_{k} = W ## Then is it always the case that...

Homework Statement I have no idea where the sum of x^2 comes from, from the information I posted. I know it must be something pretty simple but its completely going over my head. In the picture that I've attached, I am wondering where the 2431.72, 4901.66, and 3252.44 come from. Thank you...

Also would someone mind checking my work on these problems too? My answers are in BOLD 2a)Draw the truth table corresponding to $f$(X,Y,Z) = $$\pi$$M(2,4,6) ANSWER: x y z | f 0 0 0| 1 0 0 1| 1 0 1 0| 0 0 1 1| 1 1 0 0| 0 1 0 1| 1 1 1 0| 0 1 1 1| 1 2b) Write out the canonical product of sums...

Dear, I assume that a signal S is expressed as S = a*S1 + b*S2, where a, b are weight constant, and S1, S2 are the different signals. In addition, S1, S2 have similar distribution such as Gaussian or Laplacian distribution, and theirs pdf is p_S1 and p_S2. In the above...

Dear, I assume that a signal S is expressed as S = a*S1 + b*S2, where a, b are weight constant, and S1, S2 are the different signals. In addition, S1, S2 have similar distribution such as Gaussian or Laplacian distribution, and theirs pdf is p_S1 and p_S2. In the above assumption...

Homework Statement A signal E(t) is made up of three terms, each having the same frequency but differing in phase: E(t) = E0cos(ωt) + E0cos(ωt + δ) + E0cos(ωt + 2δ) It is possible to find the amplitude of the sum vector by summing each vector described as a magnitude multiplied by a...

\sum_{i=1}^{n}[i/2^i] Have looked and looked and cannot find it anywhere. EDITED: To correct mistake.

Is this true? I am studying direct sums and was wondering if the following statement holds? It seems to be true if one considers the proof of the dimension theorem, but I need to be sure, so I can steer my proof toward a particular direction. ## N(T) \bigoplus R(T) = V ## where ##V## is the...

This is a challenge problem I thought of: Given a real-valued matrix A, develop an algorithm that finds the submatrix with the greatest sum of its element. (If there's a tie, just return an arbitrary submatrix that's tied for the win.) Is there a way other than brute force?

I'm curious about whether a statement I conjecture about direct sums is true. Suppose that ##V## is a finite-dimensional vector space and ##W##,##W_{1}##,##W_{2}## are subspaces of ##V##. Let ## V = W_{1} \bigoplus W ## and ## V = W_{2} \bigoplus W ##. Then is it the case that ## W_{1} = W_{2}...

Homework Statement Compute the integral that is highlighted in MyWork.jpg using Riemann sums using left and right endpoints. Homework Equations ##x_i* = a + i Δx## ##*x_i = a + i Δx - Δx## ##Σ_{i=1}^{n} i = n(n+1)/2## ##Σ_{i=1}^{n} i^2 = n(n+1)(2n+1)/6## The Attempt at a Solution My...

Homework Statement If the product of the numbers R and 11/S is the same as their sum, find the value of S. Homework Equations N/A The Attempt at a Solution I am suspecting that the only set of 2 numbers that have the same sum and product is 2 and 2. So I guess R is 2, 11/S is...

Let $x$ be a complex number such that $$x^{2011}=1$$ and $x\ne1$. Compute the sum $$\frac{x^2}{x-1}+\frac{x^4}{x^2-1}+\frac{x^6}{x^3-1}+\cdots+\frac{x^{4020}}{x^{2010}-1}$$.

Finding Two Vectors from Given Linear Combination Homework Statement If v + w = (5,1) and v - w = (1,5), compute and draw v and w. Homework Equations v + w = (5,1) v - w = (1,5) The Attempt at a Solution I understand how to find the sum of two vectors, but I'm confused on how to find...

Problem: Through transformation with orthogonal matrix $O$, the problem $$\hat{b}=\underset{b}{\operatorname{arg min}}||y-Xb||^2$$ is equivalent to $$\hat{b}=\underset{b}{\operatorname{arg min}}||y^{*}-X^{*}b||^2$$, where $y$ and $y^{*}$ are in $\mathbb{R}^m$, $X$ and $X^{*}$ are in...

Find the exact value of the series $$\frac{1}{4!}+\frac{4!}{8!}+\frac{8!}{12!}+\frac{12!}{16!}+\cdots\cdots$$

Homework Statement I want to show that $$ \tan^{-1}(x)=\sum\limits_{n=0}^{\infty}\frac{(-1)^{n}}{2n+1}x^{2n+1}. $$ Homework Equations I start with $$ \int\frac{1}{1+x^{2}}dx. $$ The Attempt at a Solution I want to be able to do the following: $$...