Series Definition and 998 Threads

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.

In the figure below, a potential difference V = 150 V is applied across a capacitor arrangement with capacitances C1 = 12.0µF, C2 = 6.00µF, and C3 = 16.0µF. Find the following values. Here's the diagram: http://www.webassign.net/hrw/hrw7_25-28.gif I already solved this problem but I'm having...

Originally from the statistics forum but am told this is more of a calculus question. I flip 10 coins, if any of the coins land on tails, all of the coins split into 10 new coins and I flip them all again. I keep doing this until a round where every single coin lands on heads. Can I expect to...

Very basic issue here. Using: \frac{1}{1-x} = \sum_{i=0}^{\infty} x^{i} , |x|<0 Find the power series representation and interval of convergence for: f(x) = \frac{1}{(1-3x)^{2}} We have that: \frac{d}{dx}\left[\frac{1}{1-x}\right] = \frac{1}{(1-x)^{2}} = \sum_{i=0}^{\infty} ix^{i-1} ...

Homework Statement Hey guys, I'm just going through a Laurent series example and I'm having trouble understanding how they switched the index on a summation from n=0 to n=1 and then switched the argument from z^(-n-1) to z^n as well as changing the upper limit to -infinity. If anyone could shed...

Homework Statement when the test is inconclusive when p = 1? when p=1 , the sum of uk will grow bigger , to infinity , right ? Homework EquationsThe Attempt at a Solution let's say uk = 2 , uk_2 = 2 , so as uk_3 ,l uk_4 ... the sum of all of them will beocme infinity , right?[/B]

I can't articulately ask the question so I drew a diagram. In the diagram, both capacitors are equal in capacitance. The bottom inductors are both 10000 nh and the top are 100 nh. A. Will the capacitors charge at the same time? B If we switch the large inductors to the top and the small to the...

Homework Statement Hello everyone, I'm new to the great field that is Fourier analysis, and have a question about the way in which to determine if the function is a odd or even function. Given the function, of one period f(x) = { x; 0 <= x < =1, 1; 1 < x < 2, (3 -x); 2 <= x <= 3: Is...

Homework Statement Two 1.80 V batteries—with their positive terminals in the same direction—are inserted in series into the barrel of a flashlight. One battery has an internal resistance of R1 = 0.280Ω, the other an internal resistance of R2 = 0.155Ω. When the switch is closed, a current of...

Homework Statement Find the Fourier series for the following function (0 ≤ x ≤ L): y(x) = Ax(L-x) Homework EquationsThe Attempt at a Solution 1. We start with the sum from n to infinity of A_n*sin(n*pi*x/L) where An = B_n*Ax(l-x) 2. We have the integral from 0 to L of f(x)*sin(m*pi*x/L) dx...

Homework Statement Use data from your experiment to support the idea that Young's Modulus relates the material and is independent of shape and geometry whilst the spring constant is a function of the shape and geometry. The experiment involved stretching identicle springs (starting off with one...

Homework Statement I need to find the Laurent Series of Cos[\frac{1}{z}] at z=0 Homework Equations None The Attempt at a Solution I've gone through a lot of these problems and this is one of the last on the problem set. With all the other trig functions it's been just computing their...

I have attached the image with post. Answer to question is given as A. I am not getting the explanation to how can one zener diodes be in breakdown and other not. I think if the combined voltage of 150V is applied then only breakdown occurrs in both the diodes simultaneously.

Homework Statement Use any appropriate test to determine the convergence or divergence of the following series: \sum_{i=0}^{\infty} \frac{2^{i} + 3^{i}}{4^{i}+5^{i}} Homework EquationsThe Attempt at a Solution I've run it through mathematica and it told me it's convergent. However, I...

Hi, I cannot solve for the function g(t) (eq. 6) in the attached figure where there are two series resistances. My solution is incomplete. I do not know how to use Vx in this solution, which is needed because it contains h(t) found in the solution.