Sum Definition and 1000 Threads

The FT decomposes images into its individual frequency components In its absolute crudest form, would the sum of these two images (R) give the L image?

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... In Section 10.2 Cooperstein writes the following, essentially about external direct sums ... ... Cooperstein asserts that properties (a) and (b) above "characterize the space ##V## as the direct sum of...

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... In Section 10.2 Cooperstein writes the following, essentially about external direct sums ... ... Cooperstein asserts that properties (a) and (b) above "characterize the space V as the direct sum of the...

Homework Statement Question: Sum of all the solutions of the equation: ##tan^2 (33x) = cos(2x)-1## which lie in the interval ## [0, 314] ## is: (a) 5050 π (b) 4950 π (c) 5151 π (d) none of these The correct answer is: (b) 4950 π Homework Equations ## cos(2x) = 2cos^2(x) -1 ## The Attempt...

Homework Statement Roots of the equation x3 - x + 1 = 0 are a, b, and c. Determine the value of a16+b16+c16 ! Homework Equations For ax3+bx2+cx+d = 0 x1+x2+x3 = -b/a x1 * x2 * x3= -d/a The Attempt at a Solution [/B] I know how to determine the value of a + b+ c but not a^16+b^16+c^16... I...

For the function given below find a formula for the Riemann sum obtained by dividing the interval [1,5] into n equal subintervals and using the right-hand endpoint for each c subscript k. Then take a limit of thissum as n-> infinite to calculate the area under the curve over [1,5]. Below you...

Homework Statement Write a program that reads in any characters from the keyboard, sums up only characters corresponding to a digit and prints the result on the screen. The program will exit when the character 'Q' is entered (upper or lowercase). Example: Input = 9 8 q Output = The total is...

Can someone check if my Sum of All Forces is setup correctly? Problem: Diagram: http://puu.sh/o6pLY/285d7b12c1.jpg Sum of all Forces:

Compute \sqrt[n+1]{\frac{n+1}{n}}+\sqrt[n]{\frac{n}{n-1}}+\cdots+\sqrt[4]{\frac{4}{3}}+\sqrt[3]{\frac{3}{2}}+\sqrt{2}.

I'm not sure where to put this question. It is by itself pretty basic, but it's a preamble to a Laplace Transform exercise, and I'll probably want to ask some follow up questions once the current query is resolved. 1. Homework Statement Unit stair-case function: f(t) = n, \ if \ \ n-1 \leq t...

Find the sum of the first 17 terms of the arithmetic series $$8+\sqrt{7}, \ 6,\ 4-\sqrt{7}$$ $$u=8+\sqrt{7}$$ $$S_{17} =\frac{u\left(1-\frac{{6}^{17}} {u} \right)}{u}$$ My first shot at this

My professor did this exercise that I didn't quite get how she went through all of it. We have a ##U = {(x, y, z, t) : x+y+z+t = 0}## and ##B_{Im(f)} = \left[ \begin{pmatrix} 7 \\ -3 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 3 \\ -3 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 5 \\ 0 \\ 1 \\ -5...

Often in empirical studies you see statements that factor X explains some fraction of the variance in some other variable V, and thinking about what this means intuitively made me curious about the following question. Suppose you have a model where the values of some set of factors X1, X2, ...

Homework Statement If $$a_n = \sum_{r=0}^{n} \frac{1}{\binom{n}{r}}$$ Find $$\sum_{r=0}^{n} \frac{r}{\binom{n}{r}}$$ in terms of an and n 2. The attempt at a solution Let $$f(x) =\sum_{r=0}^{n} \frac{x^r}{\binom{n}{r}}$$ Then, an = f(1). Observe that f'(1) is the required sum. I was thinking...

During lecture, the professor gave us a theorem he wants us to prove on our own before he goes over the theorem in lecture. Theorem: Let ##V_1, V_2, ... V_n## be subspaces of a vector space ##V##. Then the following statements are equivalent. ##W=\sum V_i## is a direct sum. Decomposition of...

Homework Statement Find all values a\in\mathbb{R} such that vector space V=P_2(x) is the sum of eigenvectors of linear transformation L: V\rightarrow V defined as L(u)(x)=(4+x)u(0)+(x-2)u'(x)+(1+3x+ax^2)u''(x). P_2(x) is the space of polynomials of order 2. Homework Equations -Eigenvalues and...

So i want to calculate an r value 5 different times then find the mean of the 5 calculated values. I have 2,187 data points. the first line of code generates 100 random points 1-2187. The code has a bug but my major issue is it calculates r then loops again calculates r, loops again calculates...

Homework Statement Let {b k } be a sequence of positive numbers. Assume that there exists a sequence {a k}, such that a k is greater than or equal to 0 for all k, a_k is decreasing, the limit of a_k is 0 and b_k = a_k - a _(k+1). Show that the sum from k=1 to infinity of b k exists and equals...

Hello! (Wave) We suppose that a force that is given by the vector $2i+j$ is applied at an object that moves at the direction $i+j$. How can we express this force as a sum of a force that has the direction of the movement and a force that is perpendicular to the direction of the movement?

Hello, My hobby is to design algorithms especially data compression algorithms, but when I can't find a solution to my problems I usually go find myself a different problem to solve because it helps me think differently or maybe it lights a bulb about the original problem …today I stumbled on...

Let $x_1,\,x_2,\,x_3$ be the three real roots of $P(x)=x^3-2x^2-x+1$ such that $x_1>x_2>x_3$. Evaluate $x_1^2x_2+x_2^2x_3+x_3^2x_1$.

Somewhere I saw that the sum of the infinite arithmetic series \sum_{n=1}^{\infty}n = \frac{-1}{12} Why exactly is this? I thought infinite arithmetic series had no solution? Also... WHY is it negative? Seems counter-intuitive that the sum of all the NATURAL numbers is a decimal, a negative...

My current understanding of differential equations is extremely shaky, and my vocabulary is probably very incorrect, but I'm curious about something I've recently seen in some Khan Academy videos (specifically this one) and in other situations with differential equations. It seems that the...

Prove $$\sum_{n=0}^N\cos(nx)=\csc\left(\dfrac x2\right)\sin\left(\dfrac{(N+1)x}{2}\right)\cos\left(\dfrac{Nx}{2}\right)$$ I've tried working from the RHS with various identities but haven't managed to come up with anything that works. I suspect this problem involves some trigonometry that I...

Homework Statement Determine whether each of the following series is convergent or divergent. If the series is convergent, find its sum \sum_{i=1}^{\infty} \frac{6}{9i^{2}+6i-8} Homework Equations Partial fraction decomposition \frac{1}{3i-2} - \frac{1}{3i+4} The Attempt at a Solution...

Homework Statement ## lim_{n \rightarrow \infty}{\frac{1}{n^2} \sum_{k=1}^{n} ke^{\frac{k}{n}}} ## Homework EquationsThe Attempt at a Solution ## lim_{n \rightarrow \infty}{\frac{1}{n^2} \sum_{k=1}^{n} ke^{\frac{k}{n}}} \\ = lim_{n \rightarrow \infty}{\frac{1}{n^2}...

Hello, I am currently in my first year of college, and I already took calculus in high school. I was able to solve all the problems, but I feel like I didn't understand everything conceptually. When integrating dy/dx=x you get, ∫x dx=1/2x2. But what exactly happened to the dx, why did it...

Homework Statement Find ##x[n] \ast h[n]## when ##x[n] = 3 u[2-n]## and ##h[n] = 4\left( \frac{1}{2} \right)^{n+2}u[n+4]## where ##u[n-k]## is the unit step function. Homework Equations None really The Attempt at a Solution So I know this is probably simple but I am confused. So the...

Homework Statement Find the sum of the numbers between 200 and 800 inclusive, which are multiples of 6, but not multiples of 9. Homework EquationsThe Attempt at a Solution Numbers that are multiples of 6 should be: a = 6n, n ∈ ℤ and a is any multiple of six. 200 = 6n → n1 = ##\frac{200}{6}## =...

I am reading Steven Roman's book, Advanced Linear Algebra and am currently focussed on Chapter 1: Vector Spaces ... ... In discussing the sum of a set of subspaces Roman writes (page 39) ...In the above text, Roman writes: " ... ... It is not hard to show that the sum of any collection of...

Let $a,\,b,\,c,\,d\in \mathbb{R}$ with condition that $a+b\sqrt{2}+c\sqrt{3}+2d\ge \sqrt{10(a^2+b^2+c^2+d^2)}$. Prove that $a^2+d^2=b^2+c^2$.

Prove the inequality \sqrt{\frac{1\cdot 2}{3^2}}+\sqrt{\frac{2\cdot 3}{5^2}}+\sqrt{\frac{3\cdot 4}{7^2}}+\cdots+\sqrt{\frac{4032\cdot 4033}{8065^2}}<2016

Hey, Please may someone help me. How can I show that 3r(r+1) is equal to r(r+1)(r+2) - r(r-1)(r+1) and then I would find the total sum of r(r+1). Thanks in advance for any help.

Homework Statement ∑n!/(3*4*5...*n) s1=1/3 sn=1/3+2/(4*3)+3!/(5*4*3)+...+n!/(3*4*5*...n) so i multiplied the sum with 1/2sn=1/6+1/(4*3)+1/(5*4)+1/(6*5)...+1/((n+2)(n-1)) got blocked here,i don't know how to continue, help please

Hello! (Wave) The finite sequence of integers $Y_1, \dots, Y_M$ takes both positive and negative values, where $M$ is a fixed positive integer. Could you help me to find a formulation using dynamic programming that solves the problem of finding integers $i_1, i_2$ with $1 \leq i_1 \leq i_2...

Hello, I am searching for some kind of transform if it is possible, similar to a Fourier transform, but for an arbitrary function. Sort of an inverse convolution but with a kernel that varies in each point. Or, like I say in the title of this topic a sort of continuous equivalent of fitting a...

Homework Statement Show that the sum of two future-pointing null vectors is a future-pointing time-like vector, except when the two null vectors have the same direction. Conversely, show that any time-like vector can be expressed as a sum of two null vectors. For a given time-like vector the...

Why we sometimes take the area bounded by the curve is sum of positive area and absolute of negative area(e.g. ∫\int_0^2π sin(x)\, dx is equal to 4 or area of ellipse )?But sometimes we just sum positive and negative areas which is equal to 0(e.g. area of cycloid →when we integrate we get...

If we have a positive integer, how many ways can this number be written as a sum of its components? By components, I mean all numbers less than that number. For example, 5 has 6 ways to be written; 5x1, 3x1+2, 2x2+1, 2x1+3,1+4 and 2+3. In digits form; [11111, 1112, 221,113, 14, 23] So there are...

Homework Statement So I'm checking my solutions to past question and there's one bit that throws me. 1/(1+(z-1)) = Σ(-1)n(z-1)n (for 0<|z-1|<1) I don't know where the (-1)n factor came from. Is it just something that always happens that I didn't know about / forgot about, or is there some...

Homework Statement Solve \begin{equation*} 36x^2y''+(5-9x^2)y=0 \end{equation*} using the Frobenius method Homework Equations Assume a solution of the form \begin{equation*} y=\sum_{n=0}^{\infty}{a_nx^{n+s}} \end{equation*} then \begin{equation*}...

While balancing rotating mass we consider the inertia force (centrifugal force) is equal and opposite to centripetal force which causes the rotation. if both force(applied external force on rotating mass) which causes the motion and force which resist motion (inertia force) are equal and...

Is there a way to find the following sum in closed form: ∑K(N,n) , where K(N,n) is the binomial coefficient and the sum can extend over any interval from n=0..N. I.e. not necessarily n=0 to N in which case on can just use the binomial theorem.

Homework Statement Find the Fourier series defined in the interval (-π,π) and sketch its sum over several periods. i) f(x) = 0 (-π < x < 1/2π) f(x) = 1 (1/2π < x < π) 2. Homework Equations ao/2 + ∑(ancos(nx) + bnsin(nx)) a0= 1/π∫f(x)dx an = 1/π ∫f(x)cos(nx) dx bn = 1/π ∫f(x) sin(nx) The...

Evaluate \sum\limits_{k=1}^{12} {12\choose{k}}k^2 The answer is 159744.

Is there a closed form expression for the sum: Σx2/n! from 0 to N for N=∞ it is an exponential but what about the finite case?

Homework Statement Find \sum\limits_{k=0}^{n}k^2{n\choose k}(\frac{1}{3})^k(\frac{2}{3})^{n-k} Homework Equations -Binomial theorem The Attempt at a Solution I am using the binomial coefficient identity {n\choose k}=\frac{n}{k}{{n-1}\choose {k-1}}: \sum\limits_{k=0}^{n}k^2{n\choose...

this is just an arithmetic series but with a small difference. i will show that below The attempt at a solution the general arithmetic formula ## S_N=\sum_{n=1}^\infty n## for my problem ## S_N=\sum_{n=1000}^{2000} n ## i have to rewrite it so i will just add the even numbers ##...

So I'm supposed to find the exact values of the sine, cosine, and tangent of an angle by using a sum or difference formula ( i.e. sin(x+y)=sin(x)cos(y)+cos(x)sin(y) ), but this is the angle I was given: ${-13\pi}/{12}$. How do I use a sum or difference formula to get the sin, cos, and tan of that?

Maybe I just need help understanding the question ... write $ x^2 + 2xy + 2yz + z^2 $ as a sum of squares $ (x')^2 -2(y')^2 + 2(z')^2 $ in a rotated coord system. The 1st expression $ = \left[ x, y, z \right]M \begin{bmatrix}x\\y\\z\end{bmatrix} $ and I get $ M =...