Series Definition and 998 Threads

Hello and thank you for trying to help. In spite of the fact that this seems a very simple problem, I do not find myself able to get a solution. Here it goes: Let $$f(x)=\displaystyle \sum_{k=3}^\infty a_k \frac{x^k}{k(k-1)(k-2)}$$ and $$g(x)=\displaystyle \sum_{k=0}^\infty a_k x^k$$. Express...

i really need help about shunt and series resistances i just want to know if they are constant or variable ? if they are variable what make them increase or decrease?

Hiya everyone, Alright ? I have a simple theoretical question. In a decreasing geometric series, is it true to say that the ratio q has to be 0<q<1, assuming that all members of the series are positive ? What if they weren't all positive ? Thank you in advance !

According to this page: https://en.wikipedia.org/wiki/Cantor's_theorem It says: "Cantor's theorem is a fundamental result that states that, for any set A, the set of all subsets of A (the power set of A) has a strictly greater cardinality than A itself." Furthermore, it says: "Cantor's...

Homework Statement Write the Taylor's series expansion of the function f(x,y) = e-x2 sin(y) about the point (1,3). (The question doesn't specify how accurate it wants the answer to be, but based on the answer I have, it seems to me that the Taylor's polynomial should be of degree 3.)...

Homework Statement Trying to find the sum of (-1)3n+1/(2n-1)3. by using term-by-term integration on the cosine Fourier series x= L/2-4L/π2∑cos(((2n-1)πx)/L)/(2n-1)2. Homework Equations Shown below The Attempt at a Solution When integrating and substituting Lx/2 for x's sine Fourier series I...

Hi, I have a couple of questions regarding re-wiring a three phase transformer. Say you have a three phase TX with a ratio of 415:22 and you want to use it as a single phase step-up TX (excite it with a variac or something), this is a thought-experiment. If you excited only the middle leg of...

Hello all, Three consecutive elements of a geometric series are: m-3i, 8+i, n+17i where n and m are real numbers. I need to find n and m. I have tried using the conjugate in order to find (8+i)/(m-3i) and (n+17i)/(8+i), and was hopeful that at the end I will be able to compare the real and...

Homework Statement I have the circuit above. When I have the switch at A, the capacitor C1 is charging at 100μF is at 10V. I then discharge the capacitor by connecting the switch to B. I was asked to calculate the time constant. I thought the capacitors were in parallel but according to...

Homework Statement here is my problem : Homework Equations like usual, the problem is related with RLC circuits and transients The Attempt at a Solution [/B] from here, the solution is obviously wrong because from the solution, its alpha should be -300 and not -0.4...and from the...

$\textrm{a. find the power series representation for $g$ centered at 0 by differentiation}\\$ $\textrm{ or Integrating the power series for $f$ perhaps more than once}$ \begin{align*}\displaystyle f(x)&=\frac{1}{1-3x} \\ &=\sum_{k=1}^{\infty} \end{align*} $\textsf{b. Give interval of convergence...

I have a large array of solar panels, which are 12v panels. I have wired them two each in series to produce 24v at the array and carry that to a 24v charge controller which then connects to two 12v batteries wired in series for 24v, to power a 24 volt inverter. But I have observed a problem...

Does anyone know of any good references for a detailed guide designing a series pass regulator along with compensation? I'm having some trouble getting the plant transfer function and would really benefit from some book or video or application note on this topic. Even an older thread on...

Homework Statement The original problem was to find for which real numbers the series $$ \sum_{n=1}^{\infty} 2^{n} .\left( \dfrac{ n }{ n+1 } \right)^{n} x^{n} $$ converges. I used root criterion, it gave me a radius of convergence equal to 1/2. For x=1/2, I showed that the sequence converges...

İ couldn't understand the last operation, please help me.

Homework Statement An ammeter and a voltmeter are joined in series to a cell.Their readings are A and V respectively.If a resistance is now joined in parallel with the voltmeter, A)both A and V will increase B)both A and V will decrease C)A will decrease,V will increase D)A will increase,V...

Homework Statement A mass ##m## hangs from a combination of two springs, each with spring constant ##k##, connected in series. If the mass is doubled to ##2m## the mass will hang lower by a distance ##h##. If three such springs are arranged in parallel to support a mass of ##5m## what will be...

Hey guys I made an account here because I cannot understand this for the life of me. Two 95 W (120V ) lightbulbs are wired in series, then the combination is connected to a 120 V supply. How much power is dissipated by each bulb? Answer 24W The part I don't understand is why 95=(120^2)/R...

The side by side coils are round or oval, and wired together in series. Let's say the side by side coils are wound opposite (one clockwise and one counterclockwise) to match the direction of travel of the twisted coil's loops. Each of the side by side coils has the same number of turns as the...

It's been 40 years since I did any real chemistry and I'm trying to refresh my understanding of reactive metals. I'm trying to understand how to approach a question such as "What happens if you mix solutions of Sodium Hydroxide and Copper Sulfate". I know the result is Copper Hydroxide and...

Homework Statement Two Ohm's resistors in parallel consume power of 76 W and 24 W. What power will each of them consume if transfer them to the serial circuit with the same voltage of source. Sorry for my bad english translations I m not use to writing questions in English.. So what confuses...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] Hi, I was working on a the source transformation and i got to the part where there are two current sources in the circuit. The current sources were added together (giving they were going...

Homework Statement I want to find different parameters of series and parallel RLC for series RLC we have this transfer function and we know that transfer function of second order system is something like this:we can assume H0=1 but is wrong(when you use only denominator you find out that...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] Hi, I am trying to understand the 2nd equality . I thought perhaps it is an expansion of ##(1-\frac{z}{w})^{-2}## (and then the ##1## cancels with the ##1## in ##( (1-\frac{z}{w})^{-2}) -1 ) ##) in the form ##(1-x)^{-2}##...

Hi. I have this power serie (2^n/n)*z^n that runs from n=1 to infinity, and I have to show whether it's uniform konvergence on [-1/3, 1/3] or not. I hope someone can help me with this.

I'm in Calculus 2, and I have a final coming up. I did extremely well in all other sections, but this section is extremely confusing. I can represent functions into a basic MacLaurin series, and I can also take the derivative of a function and find the series through manipulation of the function...

Homework Statement In the circuit below, the RMS of the AC source is 100V, the inductive reactance is 50 ohm, the capacitive reactance is 200 ohm, the resistance is 40 ohm and the current flows in the circuit is 0.644 A. Determine the reading of the voltmeter. Homework EquationsThe Attempt...

What is the procedure for finding the unknown term(end value in this scenario) in a series? For example $$ \sum_{r=1}^{n}{2r+3} $$ My Attempt was to simply state the first four terms and then simply add the nth term as it is: 2(1)+3=5 2(2)+3=7 2(3)+3=9 2(4)+3=11 2(n)+3=2n+3...

Find derivative of y=✓{x+✓[y+✓(x+...)]}infinite. Here root comes for total inter terms

Homework Statement Consider now a sample consisting of all possible n-digit integers where n is odd. Use your answers to the first two parts or otherwise to deduce a formula for the number of palindromic numbers within this sample.Your formula should be a function of n only. [6 marks] [Hint...

Homework Statement A step voltage of 120v is applied to a series CR circuit. R = 20KΩ, C = 4µF 1. Deduce, using Kirchoff's voltage law and Laplace Transforms, an expression for the transient circuit current. 2. Using the equation obtained in 1. deduce the equations for the transient voltages...

Homework Statement Homework Equations P = k A \frac{dT}{dx} The Attempt at a Solution a) Assuming steady state transfer, energy transfers through rods at the same rate everywhere. Letting T be the temperature at the point of welding. P_1 = k_1 A \frac{T_h-T}{L} \\ P_2 = k_2 A \frac{T -...

Homework Statement Using the power series for ln(x + 1) and the Estimation Theorem for the Alternating Series, we conclude that the least number of terms in the series needed to approximate ln 2 with error < 3/1000 is: (i) 333 (ii) 534 (iii) 100 (iv) 9 (v) 201 Homework Equations ln(x+1) =...

Homework Statement Three lamps are rated 110 V, 60 W. They are connected in parallel and a capacitor is connected in series with the group. The circuit is then connected to a 230 V 50 Hz power supply. Detremine: a) The capacitance which is required to provide the correct voltage across the...

find the sum of this infinite geometric series: 1 - √2 + 2 - 2√2 + ... a.) .414 b.) -2.414 c.) series diverges d.) 2 I found that the common difference is 2, so I calculated this: S∞= -.414/-1 s∞= .414 So i got that the answer is A, but will you check this?

Hello! (Wave) I want to find the Fourier series of $f(x)=x, 0 \leq x<1$. It is a series with period $1$. In our case, the function is odd. So in order to find the Fourier series, we would find the odd extension of $f$ and then use the following formulas: $a_n=0 , \ \ \forall n \geq 0$...

What is your favorite Star Trek series and why. Who was your favorite character? I go with Next Generation because it's what I grew up on however Spock as best character.

Hello! I want to find the Fourier series for the given function $f$: $f(x)=\left\{\begin{matrix} 1, & 0<x<1,\\ 0, & 1<x<2 \end{matrix}\right.$ -> cosine series, period 4 I also want to find the graph of the function to which the series converges , for three periods and then make some...

Hello! (Wave) The following problem shall show the way with which the Fourier series can be used for the solution of initial value problems.Find the solution of the initial value problem $$y''+ \omega^2 y=\sin{nt}, y(0)=0, y'(0)=0$$ where $n$ is a natural number and $\omega^2 \neq n^2$. What...

In reviewing some calculations, I've arrived at the series: ##S(d)=-\frac 1 {d-1}+\frac 1 2 \frac{d-2}{d-3}-\frac 1 8 \frac{(d-2)(d-4)}{d-5}+\frac 1 {48} \frac{(d-2)(d-4)(d-6)}{d-7}+\dots ## Its an infinite series but because I'm interested in its values for even ##d##s, its actually a finite...

Homework Statement I am going over problems for exam study - here is the question with my submitted solution. Anything helps, just trying to correct mistakes so I can study the problems. Two capacitors C=3mF, C=2mF are initially discharged. They are connected in series and then the two ends...

Homework Statement [/B] There are three problems that I am struggling with. 1. ∑[k2(x-2)k]/[3k] 2. ∑[(x-4)n]/[(n)(-9)n] 3. ∑[2k(x-3)k]/[k(k+1)] The Attempt at a Solution On the first two I am having problems finding the end-points of the interval of convergence. I use the ratio test. 1...

Homework Statement Use a laurent series to find the indicated residue f(z)=e^{\frac{-2}{z^2}} Homework EquationsThe Attempt at a Solution So I expand the series as follows 1-\frac{2}{z^2}+\frac{2}{z^4} ... my book says the residue is 0 , is this because there is no residue term ? the...

Homework Statement "Find the recurrence relation in the power series solution for ##y''-xy'-y=0## centered about ##x_0=1##." Homework Equations ##y=\sum_{n=0}^\infty a_nx^n## Answer as given in book: ##(n+2)a_{n+2}-a_{n+1}-a_n=0## The Attempt at a Solution ##y=\sum_{n=0}^\infty a_n(x-1)^n##...

Hi Two lightbulbs in series, one with 50W one with 100W which is brighter. I have two different solutions and can't see my error. Using PR=V^2 and I^2=P/V 50/√50R1=100/√100R2 with the same current and R2=2R1. Using PR=V^2 and the same voltage across both bulbs yields 50R1=100R2 or R1=2R2. Which...

Homework Statement Determine the order of the poles for the given function. f(z)=\frac{1}{1+e^z} Homework EquationsThe Attempt at a Solution I know if you set the denominator equal to zero you get z=ln(-1) But if you expand the function as a geometric series , 1-e^{z}+e^{2z}... I...

Homework Statement WE have a thermally insulated metallic bar (from enviroment/surroundings) . It has a temperature of 0 ºC. At t=0 two thermal sources are applied at either end, the first being -10 ºC and the second being 10 ºC. Find the equation for the temperature along the bar T(x,t), in...

Homework Statement Show that ##\displaystyle \frac{1}{1+x^2} = \frac{1}{x^2} - \frac{1}{x^4} + \frac{1}{x^6} - \frac{1}{x^8} + \cdots## Homework EquationsThe Attempt at a Solution I know that the power series expansion of ##\displaystyle \frac{1}{1+x^2}## about ##x=0## is ##1-x^2 + x^4 - x^6 +...

Homework Statement expand f(z)=\frac{1}{z(z-1)} in a laurent series valid for the given annular domain. |z|> 3 Homework EquationsThe Attempt at a Solution first I do partial fractions to get \frac{-1}{3z} +\frac{1}{3(z-3)} then in the second fraction I factor out a z in the denominator...

Take the following diagram of 4 1.5V batteries connected in series to creat and net voltage of 6V (the numbers are of no significance here). If we were to short circuit the system by connecting battery 1 to battery 4 (or run the current through a load), wouldn't there be electrons traveling...