Series Definition and 998 Threads

A few months ago I posted a simple equation that shows an interesting nexus between the difference between the squares of successive integers and the sums of their roots, viz: Where y = x+1 then (x + y) = (y2 - x2) Recently I expanded this relationship as follows: Where n is any integer and y...

How to develop in series as in the image below? What does the third term signify?

Homework Statement I'm trying to calculate the Fourier Series for a periodic signal defined as: y = x 0<x<2Π y = 0 2Π≤x<3Π Homework Equations Fn = 1/T ∫T f(t)cos(kwοt + θk)[/B] cn/2 + ∑k=1k=∞(cn)cos(kwοt+θk) cn= 2|Fn| θk=∠Fn The Attempt at a Solution I got Cn =...

So I am studying chaotic dynamical systems and I need to find mutual information between two chaotic time series say x(t) and y(t). Any help would be much appreciated.

That I don't even know in which forum to post this questions shows my gaping lack of mathematics knowledge. I've just learned the derivation of the Taylor series. I'm slapping myself on the head as it's so mind-bogglingly simple, but I never learned it. The Taylor series was just 'maths magic'...

Homework Statement for d/dx(e^x) , the series should be start from 2 rather than 1 , right ? because when k = 1 , the circled part would become 0 , the series for (e^x) is 1 + x + ... Homework EquationsThe Attempt at a Solution

Homework Statement http://imgur.com/12LbqWL Part b Homework EquationsThe Attempt at a Solution Since it says the first four terms, not nonzero, the first four terms would be 0-(1/3-0)+2/9(x-2)-1/9(x-2)^2 I'm confused when it says I need to find these for x=2... Do I just plug in x=2 now and...

Homework Statement I was watching a PatrickJMT video on ratio test and he gave this problem. I solved it before he did, and he got that it was divergent. He didn't simplify it initially, so our methods of approach are different. Did I do something wrong? I checked my calculator to make sure all...

Homework Statement f(x) = x , 0 <x<1/2 1/2 , 1/2 < x <1 in this question , I am not convinced that a_ 0 = 0 for half range sine series , because i found that but , thoerically , for half rang sine series , a_ 0 must be = 0 , ,am i right ? why the value of A- 0 that i got is not = 0 ...

Hello Everyone, I will try to explain what am I doing here and I hope someone will understand. ACF - autocorrelation function I'm doing a research about non-parametric methods utility. How they fit and are useful in a different environment. I'm generating time series with different sizes of...

Mod note: Moved from a technical forum section, so missing the homework template I want to write code for this double sum in MATLAB and I have written following code: x = 100; % to calculate omega and u l = 300; % to calculate omega p = 10; omegaa= x/l; deltaH = 200; deltat =...

I'm trying to find the answer to a question similar to this posted it earlier but in the wrong section I think and not explained well. $$ \sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n \ \ \rm ?$$ Find the interval of convergence? I tried using the root test and got from 0 to 1 but when I...

Hi, I would like to learn chemistry, and I am self taught. I would like to learn chemistry to the point, where if i see a chemical equation, I then know exactly what I need to do to synthesize it, and was wondering if anyone could provide any resources for me to do that. Thank you very much...

I had a question similar to Σ0∞ (-1)^n (x)^(n/2) and attempted to solve it using the root test getting abs(√x)<1, but I've also seen some places answer it as √abs(x)<1 so am I skipping a step.

Homework Statement I need to mathematically prove that the center angle(s) (labeled as "A" in the photo below) approach what I believe to be 60 degrees (but never reach 60 degrees). We are given the values of all longer legs of each right triangle. Furthermore, the value of the length of each...

Homework Statement Solve y''+(cosx)y=0 with power series (centered at 0) Homework Equations y(x) = Σ anxn The Attempt at a Solution I would just like for someone to check my work: I first computed (cosx)y like this: (cosx)y = (1-x2/2!+x4/4!+ ...)*(a0+a1x+a2x2 +...)...

Homework Statement Homework Equations Rparellel=1/R1+1/R2... IR1=R2/R1+R2 x I The Attempt at a Solution I am unsure of how to answer d) and e) using KVL because I count 4 junctions? Where should I start?

I'm a little confused on geometric series. My book says that a geometric series is a series of the type: n=1 to ∞, ∑arn-1 If r<1 the series converges to a/(1-r), otherwise the series diverges. So let's say we have a series: n=1 to ∞, ∑An, with An = 1/2n An can be re-written as (1/2)n, which...

Homework Statement Show that ##\sum_{n=1}^{\infty}\frac{1}{n^{4}}=\frac{\pi^{4}}{90}##. Homework Equations The Attempt at a Solution ##\frac{1}{n^{4}} = \frac{1}{1^{4}} + \frac{1}{2^{4}} + \frac{1}{3^{4}} + \dots##. Do I now factorise?

Homework Statement In the following circuit, the battery has emf ε = 12.7 V. The resistors are R1 = 2000 Ω . R2 = 3000 Ω, and R3 = 4000 Ω. What is the current through resistor R2 ? Homework Equations Kirchoff's Rules V=IR The Attempt at a Solution i0 (into A) - i2 (current into resistor 2) -...

Homework Statement Hello, I'm not trying to solve this exact problem although mine is similar and I am confused on how they were able to get a -1 in the exponent from one step to another. Homework Equations I have attached a picture indicating the step that I am confused about. How are they...

How is pi/L part deduced in (n*pi*x)/L?

The criteria for testing for convergence with the alternating series test, according to my book, is: Σ(-1)n-1bn With bn>0, bn+1 ≤ bn for all n, and lim n→∞bn = 0. My question is about the criteria. I'm running into several homework problem where bn is not always greater than bn+1, such as the...

There are a few problems here but it would be helpful if The below solutions could be checked and some insight provided for the last one/any other mistakes The problem & The Solution Attempts A circuit with a 12V battery then on the row below in series with the battery is a 120nF capacitor...

Homework Statement i know that k = 0 to∞∑(1/ k) is harmonic series( we know that the sum is divergent) , how about ∑(1/ k+1 ) ? Homework EquationsThe Attempt at a Solution in my opinion , it's also harmonic series , because the sum is divergent . Am i right ?

Homework Statement a. Represent f(x)=|x| in -2<x<2 with a complex Fourier series b. Show that the complex Fourier Series can be rearranged into a cosine series c. Take the derivative of that cosine series. What function does the resulting series represent? [/B]Homework Equations...

Homework Statement Represent the function (8x)/(6+x) as a power serioes f(x)=∑cnxn Find c0 c1 c2 c3 c4 Radius of convergence R= Homework EquationsThe Attempt at a Solution I've represented this function as (8x/9)∑(-x/6)n and found I-x/6I <1 so R=6 Through pure guessing I discovered c0=0 but...

Homework Statement Solve for xy'' + y' +αy + βxy = 0 α and β are constants The Attempt at a Solution What I initially had in mind was: xy'' + y' +αy + βxy = x²y'' + xy' +αxy + βx²y = 0 y = \sum_{n=0}^\infty a_n x^{n} xy = \sum_{n=0}^\infty a_n x^{n+1} = \sum_{n=1}^\infty a_{n-1} x^{n} = a_0x...

Hello; I'm struggling with pointwise and uniform convergence, I think that examples are going to help me understand Homework Statement Consider the Fourier sine series of each of the following functions. In this exercise de not compute the coefficients but use the general convergence theorems...

Let f(x) = (1+x)-4 Find the Taylor Series of f centered at x=1 and its interval of convergence. \sum_{n=0}^\infty f^n(c)\frac{(x-c)^n}{n!} is general Taylor series form My attempt I found the first 4 derivatives of f(x) and their values at fn(1). Yet from here I do not know how to find the...

Hey Physics Forums! I am a self taught individual, who would like to learn more about physics. My goal in life is to virtually understand every physics principal we know, and become extremely good at all forms of physics. I will be reading physics books over the next 30 years, so that i can...

Homework Statement \sum\limits_{n=1}^{\infty}\frac{n-1}{(n+2)(n+3)} Homework Equations S=\sum\limits_{n=1}^{\infty}a_n (1) \lim\limits_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}\gt 1\rightarrow S\ is\ divergent (2) \lim\limits_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}\lt 1\rightarrow S\ is\...

My Calculus 2 teacher's lecture slides say: Many of the functions that arise in mathematical physics and chemistry, such as Bessel functions, are defined as sums of series. I was just wondering how this was different from the basic functions that we've already worked with. Are they not...

Homework Statement This question has four parts which may follow up from each other so I incuded all the parts. The real problem I'm having is with d Consider the function f ang g given by f (x)=( e^x+[e^-x])/2 & g (x) =( [e]^x]-[e^-x])/2 a) show f'(x) = g (x) and g'(x) = f (x) b) find the...

Homework Statement http://imgur.com/1aOFPI7 PART 2 Homework Equations Taylor series form The Attempt at a Solution My thought process is that the answer is 3 because using the geometric series equation (1st term)/(1-R) then you can get the sum. In this case R would be x+2 where x is -2 so 0...

Homework Statement \lim_{n \to \infty}\frac{(-1)^{n+1} \cdot n^2}{n^2+1} Homework Equations \lim_{n \to \infty}a_n \neq 0 \rightarrow S \ is \ divergent The Attempt at a Solution I tried L'Hopital's rule, but I could not figure out how to find the limit of that pesky (-1)^{n+1}. Edit: This...

Hi. I have a question about conservation of charge when two differently charged capacitors are connected in series. I know this is like a homework problem of introductory level of physics, but since this is not my homework, I decided to post it here. So, here is the story. There are two...

Homework Statement I am supposed to determine whether the summation attached is convergent or divergent Homework Equations Alternating Series Test Test for Divergence The Attempt at a Solution The attempted solution is attached. Using the two different tests I am getting two different answers.

Hey! :o I want to find a normal series of $D_4$ and all the composition series for $D_4$. I have done the following: $D_4=\langle a , s\mid s^4=1=a^2, asa=s^{-1}\rangle$ A subgroup of $D_4$ is $\langle s\rangle=\{s, s^2, s^3, s^4=1\}$, that is normal in $D_4$, since $[D_4:\langle...

Homework Statement Complete the proof that ln (1+x) equals its Maclaurin series for -1< x ≤ 1 in the following steps. Use the geometric series to write down the powe series representation for 1/ (1+x) , |x| < 1 This is the part (b) of the question where in part (a)I proved that ln (1+x)...

Hey! :o I want to find all the composition series for $A_4$ and $S_3\times\mathbb{Z}_2$. A composition series for $G$ is $$1=S_0\leq S_1\leq S_2\leq \cdots \leq S_k=G$$ with $S_i\trianglelefteq S_{i+1}$ and $S_{i+1}/S_i$ is a simple group, right? (Wondering) Could you give me some hints how...

In my electrical engineering textbook, in the section with voltage dividers, it says that after you combine two series resistors, then the output voltage can no longer be defined. It then said that thus the equivalence was made strictly from a voltage source standpoint. I do not understand why...

Homework Statement i know that the formula of head loss is (V^2) / 2g , where v =velocity , but , why did the author want to change it to k[(Q)^1/n ] ? Homework EquationsThe Attempt at a Solution

Homework Statement "A dollar due to be paid to you at the end of n months, with the same interest rate as in Problem 13, is worth only (1.005)^{-n} dollars now (because that is what will amount to $1 after n months). How much must you deposit now in order to be able to withdraw $10 a month...

Homework Statement A string of length L =8 is fixed at both ends. It is given a small triangular displacement and released from rest at t=0. Find out Fourier coefficient Bn. Homework Equations what should i use for U0(x) ? The Attempt at a Solution

I was wondering, are the MIT introductory series any good compared to, let's say, Halliday and Resnick ? Any opninion ?

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

Homework Statement Find the Maclaurin series for f(x) by any method. f(x)=2^x Homework Equations d/dx(b^x)= ln(b)b^x The Attempt at a Solution Ok so I basically took the derivative about 3 or so times and came out with ∑ n=0 to ∞ of ((ln(2))^n(something has to go here))/n! This much I have...

This is from an example in Thomas's Classical Edition. The task is to find a solution to ##\frac{dy}{dx}=x+y## with the initial condition ##x=0; y=1##. He uses what he calls successive approximations. $$y_1 = 1$$ $$\frac{dy_2}{dx}=y_1+x$$ $$\frac{dy_3}{dx}=y_2+x$$ ...

Homework Statement Need to show that [a,f(a,a^\dagger]=\frac{\partial f}{\partial a^\dagger} Homework Equations [a,a^\dagger]=1 The Attempt at a Solution Need to expand f(a,a^\dagger) in a formal power series. However I don´t know how to do it if the variables don´t commute.