Series Definition and 998 Threads

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.

Homework Statement Fig. 25-39 shows a 12.0 V battery and four uncharged capacitors of capacitances C1 = 1.00 µF, C2 = 2.00 µF, C3 = 3.00 µF, and C4 = 4.00 µF. If only switch S1 is closed, what is the charge on (a) capacitor 1, (b) capacitor 2, (c) capacitor 3, and (d) capacitor 4? (figure at...

Homework Statement Find the Laurent expansions of ##f(z) = \frac{z+2}{z^2-z-2}## in ##1 < |z|<2## and then in ##2 < |z|< \infty## in powers of ##z## and ##1/z##. Homework Equations Theorem: Let ##f## be a rational function all of whose poles ##z_1,\dots , z_N## in the plane have order one and...

Homework Statement Find four terns of the Laurent series for the given function about ##z_0=0##. Also, give the residue of the function at the point. a) ##\frac{1}{e^z-1}## b) ##\frac{1}{1-\cos z}## Homework Equations The residue of the function at ##z_0## is coefficient before the...

I was experimenting with resonant frequency of a series RLC circuit: 5V AC source 10 ohms resistor 100microF capacitor 46mH inductor Resonant frequency is calculated to be around 74.2Hz. So I set the AC source to resonant frequency 74.2Hz and measured the voltage across the 10 ohms resistor...

Let {a}_{n+1} = \frac{4}{7}{a}_{n} + \frac{3}{7}{a}_{n-1} where a0 = 1, and a1 = 2. Find \lim_{{n}\to{\infty}}{a}_{n} Well, seeing as it says that x approaches infinity, the difference between where points an-1, an, and an+1 are plotted on the y-axis is almost insignificant, so we can simply...

Is there any gamma decay or x-ray decay in Actinium series, Uranium series or Thorium series? On Wikipedia, it only shows alpha and beta decay, does it mean high energy photon decay (gamma or x-ray) exists in each process? Thank you! https://en.wikipedia.org/wiki/Decay_chain#Actinium_series

Consider a finite series of repeated costs C that occur at a series of times ti. Is there a solution to discount these costs by interest rate r to account for time value of money, i.e. solve for S? The times ti of each cost are unknown, but the number of costs n is known, and the average time...

Homework Statement Find \lim_{x \to 0}\frac{ln(1+x^2)}{1-cos(x)} by using series representations. Check using L'Hospitals rule. Homework Equations Taylor polynomial at x=0: \sum_{k=0}^{\infty}\frac{f^{k}(0)}{k!}(x)^{k} = f(0) + f'(0)(x) + f''(0)x^{2} +... The Attempt at a Solution Using...

Hi. I am working on a linear algebra problem that arose somewhat like this: Suppose that you are shining a light with a known intensity spectrum P(\lambda) upon a surface with an unknown reflection spectrum, R(\lambda). You have a detector to detect the total reflected light intensity, I. How to...

Somewhere I saw that the sum of the infinite arithmetic series \sum_{n=1}^{\infty}n = \frac{-1}{12} Why exactly is this? I thought infinite arithmetic series had no solution? Also... WHY is it negative? Seems counter-intuitive that the sum of all the NATURAL numbers is a decimal, a negative...

hey, sir i have a question why the current remain same in series combination of resistance?

Homework Statement I am doing #9. Homework EquationsThe Attempt at a Solution I've been looking at a lot of similar problems on the internet. The main difference between this one and them is that this one has an interval of [0,4] while they often have intervals of [0,pi] or [-pi,pi] In my...

Homework Statement Homework EquationsThe Attempt at a Solution So I am tasked with answer #3 and #4. I have supplied the indicated parenthesis of 8 also with the image. Here is my thinking: Take the Fourier series for |sin(θ)|. Let θ = 0 and we see a perfect relationship. sin(0) = 0 and...

what is the rationale of multiplying "r" to the second line of series? why does cancelling those terms give us a VALID, sound, logical answer? please help. here's a video of the procedure

Homework Statement Determine whether each of the following series is convergent or divergent. If the series is convergent, find its sum \sum_{i=1}^{\infty} \frac{6}{9i^{2}+6i-8} Homework Equations Partial fraction decomposition \frac{1}{3i-2} - \frac{1}{3i+4} The Attempt at a Solution...

Hello! (Wave) We have a sequence $(y_n)$ with $y_n \geq 0$. We assume that the series $\sum_{n=1}^{\infty} \frac{y_n}{1+y_n}$ converges. How can we show that the series $\sum_{n=1}^{\infty} y_n$ converges? It holds that $y_n \geq \frac{y_n}{1+y_n}$. If we would have to prove the converse we...

My problem : I have a function that I want to integrate, in the limit that a parameter goes to zero. I have a function ##f[x,r]## I want to compute ##F[r] = \int dx f[x,r]## and then series expand as ##r \rightarrow 0## This is impossible algebraically for me, but may be possible if I can...

Homework Statement The problem wants me to find the limit below using series expansion. ##\lim_{x \to 0}(\frac{1}{x^2}\cdot \frac{\cos x}{(\sin x)^2})## Homework EquationsThe Attempt at a Solution (1) For startes I'll group the two fractions inside the limit together ##\lim_{x...

Homework Statement Use zero- through third-order Taylor series expansion f(x) = 6x3 − 3x2 + 4x + 5 Using x0=1 and h =1. Once I found that the Taylor Series value is 49. I want to be able to check the value. On the board our teacher plugged in a value into the equation to show that the answer...

Hey guys, the question is 6.b. in the picture : http://imgur.com/FaKUMUZ Here is what I did to solve it : http://imgur.com/YrIvbTO I made these two simultaneous equations. 1875 comes from the fact that U1 + U2 = 1500 and U3 + U4 = 375. Then S4 must equal 1500+ 375(1875). I then found a formula...

I learn that we can expand the electric potential in an infinite series of rho and cos(n*phi) when solving the Laplace equation in polar coordinates. The problem I want to consider is the expansion for the potential due to a 2D line dipole (two infinitely-long line charge separated by a small...

In my book, applied analysis by john hunter it gives me a strange way of stating an infinite sum that I'm still trying to understand because in my calculus books it was never described this way. It says: We can use the definition of the convergence of a sequence to define the sum of an...

As the 2nd part of a question, we start with the Fourier sin series expansion of dirac delta function $\delta(x-a)$ in the half-interval (0,L), (0 < a < L): $ \delta(x-a) = \frac{2}{L} \sum_{n=1}^{\infty} sin \frac{n \pi a}{L} sin \frac{n \pi x}{L} $ The questions goes on "By integrating both...

Find the Fourier sin series expansion of dirac delta function $\delta(x-a)$ in the half-interval (0,L), (0 < a < L): Now $b_n = \frac{1}{L} \int_0^L f(x)sin \frac{n \pi x}{L}dx $ - but L should be $\frac{L}{2}$ for this exercise... So I would get $ \frac{2}{L} \int_0^L f(x)sin \frac{n \pi...

Homework Statement When two same lamps are connected with the same battery. Their lighting will be greater when they are connected in series or parallel? Homework Equations Series U=U1+U2+U3+... I=I1=I2=I3... Parallel U=U1=U2=U3... I=I1+I2+I3+... The Attempt at a Solution The answer is when...

Homework Statement Do the following series converge or diverge? ## \sum_{n=2}^\infty \frac{1}{\sqrt{n} +(-1)^nn}## and ##\sum_{n=2}^\infty \frac{1}{1+(-1)^n\sqrt{n}}##. Homework Equations Leibniz convergence criteria: If ##\{a_n\}_{k=1}^\infty## is positive, decreasing and ##a_n \to 0##, the...

Homework Statement Using the equality ##e = \sum_{k=0}^n \frac{1}{k!} + e^\theta \frac{1}{(n+1)!}## with ##0< \theta < 1##, show the inequality ##0 < n!e-a_n<\frac{e}{n+1}## where ##a_n## is a natural number. Use this to show that ##e## is irrational. (Hint: set ##e=p/q## and ##n=q##)...

Hello everyone, I need to calculate the radiant power of an interference pattern of a series of light wave reflections. I need a value in Watts that would plug in nicely into a photodetector's responsivity function (given in Amps/Watts) and thus giving me an estimation of the output current. I...

Mod note: Moved from Homework section I know that ##1/n^4## converges because of comparison test with ##1/n^2## (larger series) converges . how do I know ##1/n^2## converges? coz I cannot compare it with ##1/n## harmonic series as it diverges. @REVIANNA, if you post in the Homework & Coursework...

Hello everyone, I have a doubt about charging of capacitors in series. Suppose I connected two capacitors of same value, say,1 mF in series and put a bulb in series with them and applied a voltage 10V across the series. In steady state, the voltage across each capacitor will be 10/2=5V. Right...

Homework Statement The odd 2π-periodic function f(x) is defined by f(x) = x2 π > x > 0 -x2 −π<x<0 Find the coefficient bn in the Fourier series f(x) = a0/2 + ∑(an cos(nx) + bn sin(nx)). What are the values of the coefficients a0 and an and why? Homework Equations bn = 1/π ∫...

Mod note: Moved from Homework section 1. Homework Statement Understand most of the derivation of the E-L just fine, but am confused about the fact that we can somehow Taylor expand ##L## in this way: $$ L\bigg[ y+\alpha\eta(x),y'+\alpha \eta^{'}(x),x\bigg] = L \bigg[ y, y',x\bigg] +...

Power systems isn't my area of specialty and I've been doing some reading where it was stated that series voltage connections are safer than parallel connection. I don't fully understand why though. website address...

well, i have an calculus exam tomorrow and I'm 100% gona fail. I've neglected calculus so i could study for other subjects and left only 2 days to study taylor's polynomial aproximation, series and function series, the latter two are way more complicated than i expected. good thing is i can...

Homework Statement ∑n!/(3*4*5...*n) s1=1/3 sn=1/3+2/(4*3)+3!/(5*4*3)+...+n!/(3*4*5*...n) so i multiplied the sum with 1/2sn=1/6+1/(4*3)+1/(5*4)+1/(6*5)...+1/((n+2)(n-1)) got blocked here,i don't know how to continue, help please

Problem A now solved! Problem B: I am working with two equations: The first gives me the coefficients for the Laurent Series expansion of a complex function, which is: f(z) = \sum_{n=-\infty}^\infty a_n(z-z_0)^n This first equation for the coefficients is: a_n = \frac{1}{2πi} \oint...