Induction Definition and 999 Threads

Homework Statement Show via induction that the nth root of (a1 * a2 * a3 * ... an) ≤ 1/ (n) * ∑ ai, where i ranges from 1 to n. Homework Equations Induction The Attempt at a Solution Let Pn be the statement above. It is clear that P1 holds since a1 ≤ a1. Now let us assume that Pn...

Hello I'm doing a question in induction motor now. formula for Induced torque is Pgap / Ws. i have found the Pgap, but in order to find Ws, i need frequency to find ns.. so my question is, how to find frequency with only given 10hp and four pole

Let $(x_n)$ be a sequence given by the following recursion formula: $$x_1 = 3, x_2 = 7,\text{ and }x_{n+1} = 5x_n - 6x_{n-1}$$ Prove that for all $n\in\Bbb N$, $x_n = 2^n + 3^{n-1}$. Attempt: For $n = 1$, we have $2^1 + 3^0 = 3 = x_1$ TRUE For $n = 2$, we have $2^2 + 3^1 = 7 = x_2$ TRUE...

Hi, please could someone help explain how magnetic flux works in Faraday's law as I struggle with electromagnetism. From what I understand, if you have a loop of wire in a magnetic field then you get an induced current if the flux is both changing and perpendicular to the plane of the loop...

Hey I've been given an equality to solve as a bonus question with a strong hint that a like one would appear on my midterm. However, I am stumped by it, it appears quite complex to me. Any insight into how to solve this would be greatly appreciated! I'll try to type it as best I can: A student...

I'm planning on building a simple induction motor for my class project and am hoping someone might have some advice about powering the motor. I feel a little ridiculous asking but I had almost no understanding of electricity prior to the beginning of my Physics 212 class and the textbook doesn't...

Hey! I've just started to learn some mathematical induction and it's proving quite tricky. Hopefully someone could help me out a little with my questions! I don't know how to format question on this forum but I'll try my best to accurately represent it: n $$sigma$$ i * 2^i = (n-1) * (2^n+1) +...

Here is the question: I have posted a link there to this thread so the OP can see my work.

Hi, I have been told that you take say a metal board and another board (both endless and paralell) leads to the following effect: The electrons are more or less freel in motion, they move to the surface until we reach an equilibrium. The electrons are assembled at the surface. Nice...

Homework Statement Why does the Faraday Law of Induction not suffer from the inconsistency encountered with the Ampere Law? Homework Equations \oint E * dl = - (N) d/dt \intB * dA The Attempt at a Solution The Ampere Law is inconsistent with the time varying equation of...

Dear all, I have encountered an issue in understanding how microphone works and I hope you guys can assist. There are two scenarios involved. In the first scenario, there is tuning fork and a microphone. The microphone contains a small disc attached to a magnet and a fixed coil. (Please...

Homework Statement The sequence {Un} is defined by the recurrence relation Un+1 = 2Un(1-Un), n≥0, U0 = 1/4 Prove by Induction that Un = 1/2( 1 - 1/22^n )I'm sorry I didn't know how to type this any better the 2 is raised to the power of 2 and that 2 is raised to the power of n The Attempt...

I've already asked somebody through email this question, so I'll copy and paste part of my email: Basically, I'm wondering why doesn't it fall from the other axioms, and if it does in fact not fall from the other axioms (which it apparently doesn't), why the axioms can't be slightly modified...

Homework Statement Question: Use induction to prove that 3^n > n x 2^n for every natural number n ≥ 3 Homework Equations N/A The Attempt at a Solution Answer: Step 1: 3^3 > 3 x 2^3 ⇒ 27 > 24 Step 2: Assume 3^k > k x 2^k Step 3: 3^(k+1) > (k+1) x 2^(k+1) ⇒ 3 x 3^k > k x 2^(k+1) +...

Homework Statement Prove: \sum^{n}_{r=0}2r(^{n}_{r}) = 3n Homework Equations The Attempt at a Solution I proceeded by induction: Testing the base case for n=0 is correct. Moving right along to try to show: \sum^{n+1}_{r=0}2r(^{n}_{r}) = 3n+1 This is where...

Hello. I have to do an experiment on this topic, but there are many things I don't know. First of all, can you tell me what do the symbols V~ and A~ mean?

Homework Statement Hey guys. I have an electromagnetic wave traveling in the z direction and polarized in the x direction. The frequency is 1 MHz and average power density is 1 W/m^2. An antenna in the shape of a circular wire is in the xy-plane centred at the origin. I would like to use...

Prove that every n E N can be written as a product of odd integer and a non-negative integer power of 2. For instance: 36 = 22 * 9

Show that for every n∈N, 34n+2 +1 is divisible by 10 Prove by Induction. Attempt) Base Case: n = 1, 3(4(1)+2) + 1 = 730 So the base case holds true. Assume that the inequality holds for n = k 34k+2 +1 is divisible by 10 Show true for n = k+1 34(k+1)+2 + 1 34k+4+2 + 1 34 * 34k+2 + 1 81 *...

Prove that for all nEN 1^2 + 3^2 + 5^2 + ... + (2n-1)^2 = (4n^3 - n) / 3My Solution) If n = 1, 4(1)^3 - 1 / 3 = 1 so base case holds. Assume 1^2 + 3^2 + ... + (2k-1)^2 = (4k^3 - k) / 3 What next?

Hi Q 1 An electrified rod attracts pieces of paper. After a while these papers fly away. Why? My Answer: Due to the phenomenon of electrostatic induction, the paper becomes charged and will be attracted towards the rod. After some time, the charge becomes neutral and paper flies. Q...

Prove this inequality by induction for all nEN: 1/√1 + 1/√2 + 1/√3 + ... + 1/√n >= √n

On my problem sheet I got asked to prove: ## (1+x)^n = \displaystyle\sum _{k=0} ^n \binom{n}{k} x^k ## here is my attempt by induction... n = 0 LHS## (1+x)^0 = 1 ## RHS:## \displaystyle \sum_{k=0} ^0 \binom{0}{k} x^k = \binom{0}{0}x^0 = 1\times 1 = 1 ## LHS = RHS hence true for...

With mathematical induction i should prove that is true for all natural numbers:http://img.tapatalk.com/d/13/10/18/u6epesu5.jpg Im sorry beacuse i have inserted an image,but I am still not used to write it in $$ here...

1. Assuming that both the windings of a transformer is wrapped around an iron core, how is an EMF induced in the secondary winding - isn't it necessary for flux to cut through the winding in order to induce an EMF? The flux cutting through the winding would apparently be very low..as most of it...

Hi, I'm using an induction coil to heat up an electrically conductive material within the coil. However, I'm worried that adjacent electrically conductive materials, which are not within the coil will also have see a heating effect, due to induction not thermal transfer. I want to avoid this as...

Homework Statement Prove that a set with n elements has \frac{n(n-1)(n-2)}{6} subsets containing exactly three elements whenever n is an integer greater than or equal to 3. Our professor wants us to use Induction. Homework Equations P(n) = \frac{n(n-1)(n-2)}{6} n \geq 3 The...

I am having issues with my homework questions, I can get them all the way to the very alst step but i seem to consistently get stuck trying to connect them to the answer at the end. (this will make more sense when you see the problem) I'm going to post both proofs I've worked on so far one after...

I am given a statement to prove: Show (without using the Binomial Theorem) that \((1+x)^n\geq{1+nx}\) for every real number \(x>-1\) and natural numbers \(n\geq{2}\). I am given a hint to fix \(x\) and apply induction on \(n\). I started by supposing \(x\) is a fixed, real number larger than -1...

Induction Problem Related to Cars... Homework Statement A small electric car overcomes a 260N friction force when traveling 23km/h . The electric motor is powered by ten 12-V batteries connected in series and is coupled directly to the wheels whose diameters are 57cm . The 240 armature...

Homework Statement Ʃ 1/√k ≥ 1/√n (under sigma should be "k=1" and above should be "n", and n is a positive integer) Homework Equations The Attempt at a Solution I. Base case when n=1 is correct. II. Inductive Hypothesis: Assume true for k=m, where k<m<n, m is a positive...

Show by induction that (2n-1)!/(2n)! <= 1/(3n+1) for all n Homework Statement Show by induction that (\frac{1\cdot3\cdot5\cdot\cdot\cdot(2n-1)}{2\cdot4\cdot6\cdot\cdot\cdot2n})^2 \leq\frac{1}{3n+1} for n=1,2,3, ... The Attempt at a Solution It might not really be relevant, but I've...

prove by Induction that n! ≥ 2^(n-1) n ≥ 1

Hello. I am reading an introduction to induction example, and I am having the hardest time trying to determine what exactly happened in the proof. Can somebody please help? How can ##3^{k-1}## + ##3^{k-2}## + ##3^{k-3}## all of a sudden become ##3^{k-1}##+##3^{k-1}##+##3^{k-1}## and how can be...

Hello Guys can you tell me how do i go about this question: Question Prove by Induction that for every positive integer n. $$3^{2n} -1$$ is divisible by 8

Hi, inductance is the property of a conductor by which a change in current in the conductor "induces" (creates) a voltage (electromotive force) in both the conductor itself (self-inductance). --wikipedia From what I understand, the inducing happens due to the resulting change in magnetic field...

Use strong induction to prove that if G is connected and every vertex has even degree that G has a Eulerian Circuit. a)verify the base case where G has no edges - done b)Write down the strong induction hypothesis that asserts the statement is true for all graphs that meet the hypotheses and...

Stuck on the induction step,please help

Homework Statement Prove; n^2 > n+1 for n = 2,3,4 by Induction Homework Equations The Attempt at a Solution p(n)= P(2) 2^2> 2+1 --> 4>3 Induction step: P(n+1): (n+1)^2 > (n+1) +1 (n+1)^2> n+2 n^2 + 2n + 1 > n+2 | -n n^2 +n + 1> 2 | -1 n^2 +n > 1 Is this correct, and how...

Hello everyone, One very basic thing about this phenomenon is not very clear to me. If a conductor moves in a region of uniform magnetic field, would it have an EMF induced across it? I'm confused because as per Faraday's law, a change in flux through the conductor is necessary for EMF to be...

It is a simple exercise to prove using mathematical induction that if a natural number n > 1 is not divisible by 2, then n can be written as m + m + 1 for some natural number m. (Depending on your definition of odd number, this can either be stated as "every number is even or odd", or as "every...

This is from a functional equation , i think there is no points in posting it here this is what i ant to prove the functions is from N to N . let x be a natural number i want to prove that f(x)=x^2 By induction suppose that f(x)=x^2 f(0)=0 holds (from the functional equation) i want...

I'm trying to calculate the power required from forced induction with this equation; W˙=m˙CpT1ηc⎡⎣(P2P1)(γ−1γ)−1⎤⎦ However I seem to be getting rather low results for work ~0.8W I have done my calculations in this spreadsheet. Any ideas where I've went wrong? thanks [SIZE="6"] Note...

So I am having a bit of trouble with a proof by induction that I need to write. The problem is to prove that the conjugate of the product g1 * ... * gm equals the product of the conjugates of g1 ... gm. This is for g1 ... gm complex numbers. I have proven this for m = 2, by simple calculation...

We wish to show that $3^n > n^3 \, , \ \forall n \geqslant 4 $. Base case $n = 4$ yields $3^4 = 81 > 4^3 = 64 $ Assume the inequality holds for $n = p $ i.e. $3^p > p^3$ for $p \geqslant 4$. Then $3^{p+1} > 3p^3$ $p \geqslant 4$ implies $3p^3 \geq 192$, as well as $(p+1)^3 \geqslant 125$...

Where and how can I find these two papers ? P. Debye, Physik. Z., 1920, 21, 178 H. Falckenhagen, Physik. Z., 1922, 23, 87 Thank you. Regards

Hi, I devised this problem for myself as part of a bigger question that I'm working on, and am having trouble solving it. I think it involves a nested induction proof but I am not sure how to start. A tip on how to begin would be much appreciated. Thanks -Patrick Homework Statement S_0 =...

Homework Statement long wire of radius R0 carries a current density j given by Find the magnetic induction B inside and outside the wire. Homework Equations Current density: ##J=\frac{I}{A}## Ampere's law: ##\oint B.dl = \mu_0 I_{enc}## The Attempt at a Solution For the magnetic field...

Homework Statement Find all natural numbers such that 2n ≥ (1+n)2, and prove your answer. 2. The attempt at a solution I can see this is true for n=0 and n>5. I try to prove this using induction as follows 20 =1≥ 1=(1+0)2 base case: 26 =64≥ 49=(1+6)2 so it is true for n=6 and suppose 2n...

1. a. coil is moved up and down in the same direction of flux. b. coil is rotated around an axis that is parallel to the flux. c. coil is rotated to the direction of the flux like a dynamo. 2. Electromagnetic inductions laws. 3. I'm really having a hard time...