Series Definition and 998 Threads

I needed to learn LMS imagine lab 14 software but I cannot find any tutorial video on youtube which explains everything from the scratch. Please help me out..

Homework Statement Find the power series in x for the general solution of (1+x^2)y"+6xy'+6y=0. Homework Equations None. The Attempt at a Solution I got up to an+2=-an(n+3)/(n+1) for n=1, 2, 3, 4, 5, 6... a3=-2a1 a4=0 a5=3a1 a6=0 a7=-4a1 a8=0 The answer in the book says y=a0sigma from m=0 to...

Hiz lets assum we have a load fixed on the roter of a the 'DC series motor' in the attached photo, where: Vt: DC source voltage (constant) Lf: field's inductive resistance (will be neglected) Rf: field's resistant Ra: Armature resistance Ia= Armature current, If: field current M: back emf (Ea)...

i watched a lot of videos and read a lot on how to choose it, but i what i can't find anywhere is, what's the physical significance of the a, if we were to draw the series, how will the choice of a affect it?

Homework Statement Find the Taylor Series for f(x)=1/x about a center of 3. Homework EquationsThe Attempt at a Solution f'(x)=-x^-2 f''(x)=2x^-3 f'''(x)=-6x^-4 f''''(x)=24x^-5 ... f^n(x)=-1^n * (x)^-(n+1) * (x-3)^n I'm not sure where I went wrong...

So, I have been trying to come up with a general solution for dI/dt in an RLC circuit. I have attached the work I have done so far. I don't know where but I am making a mistake and the waveform is not coming out right. Would really appreciate a look over my work to see if I made any obvious errors.

Hello, I have used Greiner's "Quantum Mechanics: An introduction" and found it to be awesome, bridging the ga between undergraduate and graduate courses. So, I am thinking of buying some of Greiner's book to use for my other courses and I wanted to ask you what your opinions about the books in...

Homework Statement determine whether the series below converges. ##\sum_{n=1}^\infty 2^n.n+1,√(n^4+4^n.n^3)## Homework EquationsThe Attempt at a Solution

I have this series $$\sum_{n = 1}^{\infty} \frac{\ln\left({n + 4}\right)}{{n}^{\frac{5}{2}}}$$ which I need to find whether it converges or diverges. I can use the limit comparison test and set $a_n = \frac{\ln\left({n + 4}\right)}{{n}^{\frac{5}{2}}}$ and $b_n = \frac{1}{{n}^{\frac{5}{2}}}$...

Prove \frac{10}{\sqrt{11^{11}}}+\frac{11}{\sqrt{12^{12}}}+\cdots+\frac{2015}{\sqrt{2016^{2016}}}\gt \frac{1}{10!}-\frac{1}{2016!}

I have this limit: $$\sum_{k = 1}^{\infty} {(\frac{e }{3})}^{k}$$ Which method can I use to find if it converges or diverges?

Hello, I'm working on my kids ride on cars. He has two of them. On the first it was 6V and came with one motor on one wheel. I updated it to 2 motors, one on each wheel and 12Volts. I put in a DPDT switch so he could select high and low. On high the motors are run in parallel and on low they...

I am a 12th grade student. I am new to this series and i know that these are great books. i am going to buy 3 books. the basics , introduction to algebra, introduction to geometry is it necessary to buy solution manual. is it ok to buy these three books for the beginners what about concept...

Homework Statement Hi, I have to find the RMS value of the inifnite series in the image below. Homework Equations https://en.wikipedia.org/wiki/Cauchy_product Allowed to assume that the time average of sin^2(wt) and cos^2(wt) = 1/2 The Attempt at a Solution So to get the RMS value I think I...

Find the sum of this series: $$ \sum_{n=1}^\infty \frac{n}{(n+1)!} $$ I'm really struggling with this one.. Any help will be highly appreciated. Thanks you.

Homework Statement If the nth partial sum of a series ##\sum_{n=1} ^\infty a_{n}## is ##S_{n} = \frac {n-1} {n+1}## Find ##a_{n}## and ##\sum_{n=1}^\infty a_n## Homework Equations ##S_{n} - S_{n-1}= a_{n}## ##\lim_{n \rightarrow +\infty} {S_{n}} = \sum_{n=1}^\infty a_n = S## The Attempt at a...

The problem is to find the general term ##a_n## (not the partial sum) of the infinite series with a starting point n=1 $$a_n = \frac {8} {1^2 + 1} + \frac {1} {2^2 + 1} + \frac {8} {3^2 + 1} + \frac {1} {4^2 + 1} + \text {...}$$ The denominator is easy, just ##n^2 + 1## but I can't think of...

Show that in 10 consecutive numbers there is at least one number which is co-prime to other 9 numbers.

1. The problem: Ive been all afternoon struggling with this doubt. Its a bit more teoric than the rest of the exercices i did and i just can't seem to get around it so here it goes ...

Good afternoon people. Recently I started taking a course at my college about Fourier series but I got extremely confused. Here's what's going on. In school we were asigned to use the symmetry formulas to find the Fourier series of the following: f\left ( t \right )=\begin{cases} 1 & \text{ if...

We had integrals, so we have to have series as well. Here are 10 easy to difficult series and infinite products. Up to you to find out the exact sum. Rules: The answer must be a finite expression. The only expressions allowed are integers written in base 10, the elementary arithmetic...

hi, If you look at my attachment you can see that the book express that for the situation of x=+,-(1/L) we need further investigation. It means being converged or diverged is not precise. I would like to ask: Is there remarkable proof that if x=+,-(1/L) convergence or divergence is not...

Homework Statement Classify the singularities of ##\frac{1}{z^{1/4}(1+z)}## Find the Laurent series for ##\frac{1}{z^2-1}## around z=1 and z=-1 Homework EquationsThe Attempt at a Solution So for the first bit there exists a singularity at ##z=0##, but I'm confused about the order of this...

Do (i), (ii) and (iii) apply to conditionally convergent series as well? I feel like they don't. But the book seems to say that they do because it doesn't "state otherwise".

Homework Statement Classify the singularities of ##\frac{1}{z^2sinh(z)}## and describe the behaviour as z goes to infinity Find the Laurent series of the above and find the region of convergence Homework Equations N/A The Attempt at a Solution I thought these two were essentially the same...

Consider a sequence with the ##n^{th}## term ##u_n##. Let ##S_{2m}## be the sum of the ##2m## terms starting from ##u_N## for some ##N\geq1##. If ##\lim_{N\rightarrow\infty}S_{2m}=0## for all ##m##, then the series converges. Why? This is not explained in the following proof:

Homework Statement From the given ans , i knew that it's conditionally convergent (by using alternating test) i can understand the working to show that it's conditionally convergent . But , i also want to show it as not absolutely convergent ... Homework EquationsThe Attempt at a Solution...

Homework Statement Here is my equation that I want to find bs values Homework EquationsThe Attempt at a Solution I convert sin to cos. for bs at s=0 I get and if s is not zero I can't derive a clear answer for bs. but in electronic engineer book that I read it wrote

Homework Statement This is for a differential equations class I'm taking and we're talking about the method of Frobeneus, Euler equations, and power series solutions for non-constant coefficients. The ODE is: 6x^2y''+7xy'-(1-x^2)y=0 I need to find the recurrence formula and I keep running into...

Hello! I have rather simple problem, but I can't find somehow answer for it: There are two springs in series, let's say spring 1 and spring 2. Springs are attached and spring 2 is attached to ground. In the beginning springs are not stretched. Let's say springs have spring constants k1 and k2...

I have some time series data of the absorbance of Br2 formation using UV Vis spectroscopy and I need to figure out the extinction coefficient/ absorptivity. The overall reaction is BrO3-+5Br- +6H+-->3Br2+3H2O which is expcted to go to completion I know that the equation relating absorbance to...

Homework Statement Here is my question Homework Equations I don't know with what formula does the book find Fourier series? The Attempt at a Solution

I am interested in learning about the classical mechanics, quantum mechanics, and thermodynamics as my current research in the mathematics and microbiology will involve them. I found Landau/Lifshitz series on Amazon, which seems to cover the main branches of physics. Unfortunately, I did not...

Today I had a maths exam with a question which was worded something like: Write ##sin(3x-x_0)## as its Fourier representation. By doing a suitable integral or otherwise, find the possible values of its Fourier coefficients. You may find the following useful: ##sin(\alpha-\beta) =...

Homework Statement This is for differential equations with nonconstant coefficients and I wasn't so great at series and sequences in calculus so when I came across this example problem I wasn't sure how they got to their final form. If someone could explain it to me that would be really...

Homework Statement Cassify the singularities of e^\frac{1}{z} and find the Laurent series Homework Equations e^\frac{1}{x} =\sum \frac{(\frac{1}{x})^n}{n!} The Attempt at a Solution Theres a singularity at z=0, but I need to find the order of the pole So using the general expression for the...

I was recently researching into some string theory when i came across the following summation: The sum of all natural numbers is -1/12, now I'm still wrapping my head around the context of the application within critical string dimensions, but is this summation valid? And if not, why it being...

Hi all, I am very confused about how one can find the upper bound for a Taylor series.. I know its general expression, which always tells me to find the (n+1)th derivative of a certain function and use the equation f(n+1)(c) (x-a)n+1/(n+1)! for c belongs to [a,x] However, there are...

hi I have a random set of time series data that is calculated after applying an algorithm to a main random time serie data, and really need to extract all the possible characteristics from the set. The goal is to measure those characteristics and perform some statistical graphs based on those...

Homework Statement How are the coefficients of the Fourier series modified for a function with a period 2πT? Homework Equations a0 = 1/π ∫π-π f(x) dx an = 1/π ∫π-π f(x) cos(nx) dx bn = 1/π ∫π-π f(x) sin(nx) dx The Attempt at a Solution I tried letting x= t/T so dx = dt/T and the limits x = ±...

Find the sum for the series $$\frac{5}{3}+2+\frac{12}{5}+...$$ This equals $$\frac{25}{15}+\frac{30}{15}+\frac{36}{15}+...$$ So the numerator increases by 4+k from the previous numerator But unable to set up $$\sum_{k+1}^{\infty}f(x)$$ The series should go to $\infty$ since the terms only...

The adagium of most quantumphysics-afficionado's is: "Shut up and calculate" - 'learn the formalism'. So I started with Leonard Susskind's 'Theoretical minimum' textbooks. So now I know a little (very little) about the formalism, I started to wonder to which extent I have to go to educate...

Here is a question that I have a problem with, It doesn't seem to have a solution: An increasing sequence that is made of 4 positive numbers, The first three of it are arithmetic series. and the last three are geometric series. The last number minus the first number is equal to 30. Find the sum...

Homework Statement The following function is periodic between -π and π: f(x) = |x| Find the Coefficients of the Fourier series and, by examining the Fourier series at x=π or otherwise, determine: 1 + 1/32 + 1/52 + 1/72 ... = Σ∞j=1 1/(2j - 1)2 Homework Equations f(x) = a0/2 + ∑∞n=1 ancos(nx) +...

Homework Statement Here is the problem description: Develop an Excel file that given a set of data from an RTD pulse injection will determine the model parameters of the following schematics, and then predict the conversion in a CONTINUOUS reactor with a n-order reaction (where n is not equal...

My son has just started learning about number series and has managed to do all of his homework except for two questions that have him and me stumped. To give you some idea of the level he's at most of the questions were simple number series.. eg Find the nth term in 9, 2, -5, -12 to which the...

Homework Statement we know that a2 , a4 ,a6 (even number ) = 0 , but when a1 , a3 , a5 (odd numbers) , the answer of an alternate between positive and negative ... in the second circle , the author represent it with (-1)^(n+1) , i don't think this is correct , this is because when n=3 , an =...

Homework Statement The optical power of a HeNe -laser is ##P_0 = 5.0mW## and the wavelength ##\lambda = 633nm##. The emitted light is linearly polarized. As the laser beam travels through two in-series -polarizers, the power detected behind the second polarizer ##P_2 = 1mW## . If the first...

[Note: Thread has been moved to the homework forums by a mentor] This is the Given problem This is my solution part 1 - What I did here is I series the R3 and R4 (R3 + R4), and I parallel the R34 to R5 (most of the calculation are from the calculator) This is my solution part 2 The...

Given the Laplace's equation with several boundary conditions. finally i got the general solution u(x,t). One of the condition is that: u(1,y)=y(1-y) After working on this I finally got: ∑An sin(π n y )sinh (π n) = y(1-y) However, i was asked to find An, by not using Fourier series...