Summation Definition and 610 Threads

Homework Statement Find the sum to n terms of the series whose rth term is 3r - 2r Homework Equations The Attempt at a Solution So I tried this rlog3 - rlog2 = n(n+1)/2 log3 - n(n+1)/2 log2 then I realized this was kind of useless, the only thing I could get from this is n(n+1)/2 log...

The title pretty much says it all, does anyone know infinite series summations that are equal to 1/5 or 1/7?

Hellow! I want you note this similarity: \\ \int xdx=\frac{1}{2}x^2+C \\ \int x^2dx=\frac{1}{3}x^3+C \\ \sum x\Delta x=\frac{1}{2}x^2-\frac{1}{2}x+C \\ \\ \sum x^2\Delta x=\frac{1}{3}x^3-\frac{1}{2}x^2+\frac{1}{6}x+C Seems there be a connection between the discrete calculus and the...

Homework Statement Hi When I want to take the divergence of a rank-2 tensor (matrix), then I have to apply the divergence operator to each column. In other words, I get \nabla \cdot M = (d_x M_{xx} + d_y M_{yx} + d_zM_{zx}\,\, ,\,\, d_x M_{xy} + d_y M_{yy} + d_zM_{zy}\,\,,\,\, d_x M_{xz} +...

Obviously it makes sense when considering the force of weight and the fact that the object is not moving up or down, but what is it composed of? What I mean is, the ground you are standing on is made of molecules bonded through the electromagnetic force, right? But those bonds are parallel to...

The Euler-Maclaurin summation formula and the Riemann zeta function The Euler-Maclaurin summation formula states that if $f(x)$ has $(2p+1)$ continuous derivatives on the interval $[m,n]$ (where $m$ and $n$ are natural numbers), then $$ \sum_{k=m}^{n-1} f(k) = \int_{m}^{n} f(x) \ dx -...

Hi there, i hope someone can help me. I am just unsure how to proceed with this problem. Homework Statement The question and diagram can be found in the attached image. I am looking for assistance on part (ii) Homework Equations 1. Summation of Moment = 0 2. Summation of forces along x -...

Please see the attached pic.

Question http://puu.sh/52zAa.png Attempt http://puu.sh/52AVq.png I've attempted to use Riemann sums and use the integral to prove the inequality, not sure if this was the right approach to start with as I am now stuck and don't see what to do next. For part (b), I know that if (2√n...

Homework Statement If $$\csc\frac{\pi}{32}+\csc\frac{\pi}{16}+\csc\frac{\pi}{8}+\csc\frac{\pi}{4}+\csc\frac{\pi}{2}$$ has the value equal to ##\cot\frac{\pi}{A}## then find A. A)61 B)62 C)63 D)64Homework Equations The Attempt at a Solution Writing cosec in terms of sin and taking the LCM to...

Hi, I am struggling trying to find the (equation of the) pdf of the sum of (what I believe to be) two non-central chi-squared random variables. The formula given on wikipedia (http://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution) shows that the random variable associated with...

i want to use the Fourier method to fins an summation for y(x)=Absolute value(sin(x)) -pi<x<pi i know that cos(pi*n)=(-1)^n and get why they use cos(pi*(n+1))= (-1)^(n+1) but why is then cos(pi*(n-1)) also (-1)^(n+1) (see attachment) THANX!

Hi PF, I am working on a parallel reduction code to sum up approximately 1 million 32-bit floating point numbers. The serial part running on each processor uses Kahan summation, no problems there. My problem is that this produces several sum/compensation pairs that now need to be added...

Homework Statement I'm trying to derive the PGF for the Binomial. The Attempt at a Solution I have it whittled down to \sum^{n}_{x=0}(nCx)(\frac{sp}{1-p})^x I just don't know how to simplify this further. Any help is most appreciated.

Homework Statement Homework Equations so i kno the formula for the for the sum of the first N positive integers when i = 1The Attempt at a Solution i kno the answer = [SIZE="4"]n^2(n+1)/2 but could someone explain step by step how you reduce it to get the final answer? as if I'm in...

Homework Statement let a_{i}=x^{i} and b_{i}=1\div i ! and c_{i}=(-1)^{i} and suppose that i takes all interger values from 0 to ∞. calculate a_{i}b_{i} and calculate a_{i}c_{i} Homework Equations i know that in suffix notation a_{i}b_{i} is the same as the dot product as when you have to...

sigma(1/n) Is there a formula for it?

I've been doing some work with finding the LCM of consecutive integers (1-n) and the number of factors in such an LCM. It's become easy to construct an LCM and find the factors when n is given. However, to deconstruct a given LCM and find n is proving difficult. I eventually would like to find...

Prove that: $\displaystyle\sum_{k=0}^n \frac{\cos(k x)}{\cos^kx} = \frac{1+(-1)^n}{2\cos^nx} + \dfrac{2\sin\big(\lfloor\frac{n+1}{2}\rfloor x\big) \cos\big(\lfloor\frac{n+2}{2}\rfloor x\big)} {\sin x\cos^n x} \qquad\qquad (\frac{2x}{\pi}\not\in \mathbb Z)$ *note: $\lfloor x\rfloor$ is floor...

\hbox {Is }\;\sum_{i=1}^{\infty}\sum_{j=1}^{\infty} A_{i,j}B_{i,j}=\sum_{i=1}^{\infty}\sum_{j=1}^{\infty}A_{i,j} \sum_{i=1}^{\infty}\sum_{j=1}^{\infty}B_{i,j}\;\hbox{?} \hbox {Is }\;\sum_{i=1}^{\infty}\sum_{j=1}^{\infty}...

Homework Statement Find a formula for \sum (2i-1) =1+3+5+...+(2n-1) Homework Equations The Attempt at a Solution \sum(2i-1)=(1+2+3+...+2n)-(2+4+6+...+2n) =(1+2+3+...+2n)-n(n+1) I'm unsure what to do with 1+2+3+..+2n ?

Hi all, I have an all time doubt here. We know that if r.v z = x + y where x and y are 2 random sequences having corresponding pdfs p(x) and p(y), the pdf of z, p(z) = convolution ( p(x),p(y) ). I have seen the derivation for the continuous case although not thorough how to prove it. I...

How to write something similar to the following Or is it better to write $$\sum_{n=k ,m=1}^{k+1}$$

Prove that 1/(1*2*3) + 1/(2*3*4) + ... + 1/(n*(n+1)*(n+2)) = 1/4 - 1/(2*(n+1)*(n+2) .

Here is the question: I have posted a link there to this topic so the OP can see my work.

So i realize that the integral of [f(x)dx] is pretty much the height of the rectangle f(x), multiplied by the width dx. But that is the area of 1 infinitesimally skinny rectangle. How does the integral sign add up an infinite amount of rectangles? I've taken cal 2 so if you could show what the...

Here is the question: I have posted a link there to this topic so the OP can see my work.

M_{K}=\frac{1}{2^{k+1}-2}\sum_{i=0}^{L-1}\sum_{l=1}^{K}\binom{K}{l}h_{i}i^{l}M_{K-l} M_0=1 and the size of h_i is L. I tried to compute this summation in matlab, my attempt is as following: clear h=[ (1+sqrt(3))/4 (3+sqrt(3))/4 (3-sqrt(3))/4 (1-sqrt(3))/4]'; % for simplicity i take...

Homework Statement Let ## n \geq 2## be a fixed integer. ##f(x)## be a bounded function defined in ##f:(0,a) \rightarrow R## satisfying f(x)=\frac{1}{n^2}\sum_{r=0}^{(n-1)a} f\left(\frac{x+r}{n}\right) then ##f(x)## = a)-f(x) b)2f(x) c)f(2x) d)nf(x) Homework Equations The...

Hello, I would very much like someone to please clarify the following points concerning tensor summation to me. Suppose the components of a tensor Ai j are A1 2 = A2 1 = A (or, in general, Axy = Ayx = A), whereas all the other components are 0. Is this a symmetrical tensor then? How may Ai j be...

Homework Statement How can I compute the sum An example to calculate \sum_{i=1}^n\sum_{j=i+1}^n(i+2j)?? I only have an example where n=1 and it gives a sum of 0 (why?) Maybe with n=3, what would the expanded form look like? Homework Equations I know how to do double sums, but...

Homework Statement Find Ʃ(product) with k=1 as the lower limit, and 50 as the upper limit. The formula is k/(k+2)Homework Equations The Attempt at a Solution I noticed a pattern where the first few numbers are: 1/3, 2/4, 3/5, 4/6, 5/7 The denominator should cancel with the numerator of the next...

Hii All, Can anyone give me a hint to evaluate $$\sum_{n=1}^{\infty}\frac{a^{n}}{n^{1-m}}$$; Here $$0<m,\,a<1$$. Please note that the summation converges and $$< \frac{a}{1-a}$$. A tighter upper bound can be achieved as $$1+\int_{1}^{\infty}\frac{a^{x}}{x^{1-m}}dx$$. Is there any way to...

Given S, an Infinite Series Summation, find \frac{1728}{485}S S=1^2+\frac{3^2}{5^2}+\frac{5^2}{5^4}+\frac{7^2}{5^6}+... I found out the formula for (r+1)th term of the series, hence making the series asS=1+\sum_{r=1}^{\infty}\frac{(2r+1)^2}{(5^r)^2} Now I have a hard time guessing what to do...

Hello All, I have what I think an easy summation, but I haven't worked with math for very long - I don't know the term which I should search the internet for in order to solve the problem and so I would be very thankful if you help me get the constant C out of the summation...

I need simplify this equation: Ʃwixiyi - (ƩxiwiƩyiwi)/Ʃwi Into an equation of the form: Ʃ(something - something)yi I am pretty sure the first something is xiwi, but I have no idea what the second something would be... Any help would be greatly appreciated. Thanks!

Find the sum upto n terms: 1.3.5+3.5.7+5.7.9....tn I solve it this way: tn=(2n-1)(2n+1)(2n+3) Now can I take summation on both sides? How? I mean when I add 2 on both sides the resultant is 0(2-2=0).Similarly the resultant summation will be zero? And if I take summation I get...

(Was posted in general physics forum also) I am currently reading Roger Penrose’s “Road to Reality”. In section 4.3, Convergence of power series, he refers to the sum of the series: 1 + x2 + x4 + x6 + x8 + ... = 1/(1-x2) Of course, this is true for |x| < 1, beyond which the series...

Hi everybody, I am just trying to find a decent identity that relates the sum $$\sum_{k=0}^{n}a_kb_k$$ to another sum such that ##a_k## and ##b_k## aren't together in the same one. If you don't know what I mean, feel free to ask. If you have an answer, please post it. Thanks in advance!

Homework Statement I am confused about what happens to the index of summation when I differentiate a series term by term. Let me show you two examples from my diff eq book (boyce and diprima) which are the primary source of my confusion: Homework Equations From page 268: The function f is...

Hi all, I found this "identity" online on Wikipedia, and realized that it would actually come in pretty useful for me, if only I could prove that it is true. Can you guys help me on that?: $$\sum_{k=1}^nk^m=\frac{1}{m+1}\sum_{k=0}^{m}\binom{m+1}{k}B_k\;n^{m-k+1}$$ where ##B_k## denotes the kth...

I can do this derivation the old fashioned way, but am having trouble doing it with einstein summation notation. Since \vec{B}=\nabla \times \vec{a} \vec{B}=\mu_{0}/4\pi (\nabla \times (m \times r)r^{-3})) 4\pi \vec{B}/\mu_{0}=\epsilon_{ijk} \nabla_{j}(\epsilon_{klm} m_{l} r_{m} r^{-3})...

This is a C++ class to be used for summation of doubles (floating point). It uses an array of 2048 doubles indexed by exponent to minimize rounding errors by only adding numbers that have the same exponent. NUM::NUM - array is cleared out when an instance of NUM is created NUM::clear() -...

Hi! I'm currently taking a fairly early stats course, and I'm having a bit of a hangup learning exactly how to use "moments" properly. My general solution whenever I run into problems internalizing things is to do a bunch of easy problems, and to show it from the ground up. This is my...

Hi, I have been trying to solve this difficult problem for some time and I thought of at least two ways to prove it but to no avail...the second method that I thought of was to employ binomial expansion on the denominator and that did lead me to the result where it only has x terms in my final...

Homework Statement Prove the Poisson summation formula. Homework Equations The Attempt at a Solution [SIZE="5"]Correction to image below: the very last line of the theorem (italicized) should say f hat is the Fourier transform, not f(n). Does this proof make sense and is...

\[\sum_{n=1}^{9999}\frac{1}{(\sqrt{{n+1}}+\sqrt{n}\,\,)(\sqrt[4]{n+1}\,\,+\sqrt[4]{n}\,\,)}\]

Homework Statement Please help me confirm my answer. A shop owner wants to hang a sign of mass 200 kg which is supported by which is supported by a uniform 155 N beam. What is the tension in the guy wires and the horizontal and vertical forces that the wall applies to the beam? The length...

Please see attached image. I don't understand how is it so. :confused: (Attempt): I already thought very hard, and obviously for this kind of mathematical rules, if i don't know the concept, i can't really make any attempt right? Just give me some hint then. Thanks.

Homework Statement A house painter stands 3 m above the ground on a 5.0 m long ladder that leans against the wall at a point 4.7 m above the ground. The painter weighs 651 N and the ladder weighs 140 N. Assuming no friction between the house and the upper end of the ladder, find the force of...