Series Definition and 998 Threads

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...

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...

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.

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.