Induction Definition and 999 Threads

Homework Statement For the sequnce an defined recursively, I have to determine the limiting value, provided that it exists. a1=2 and a(n+1) = 1/(an)^2 for all n Homework Equations The Attempt at a Solution Ok, so I 've done problems like this but the a(n+1) was biggger than...

Hi everybody, I want to buy a 3kW induction cooktop. The one I intend to buy requires a power source at 220V/60Hz. However, in my country, the main power is 220V/50Hz. Does this difference in frequency cause any incompatible problems? Can I use the induction cooktop in my country? Thanks.

Hello, I have a subgroup S=\left\langle A \right\rangle generated by the set A, i.e. S=\left\{ a_1 a_2 \ldots a_n \;|\; a_i \in A \right\}. When I need to prove by induction on n some property of S, what should I choose as the base case of induction? n=1, or simply n=0 ? If the answer is n=0...

Homework Statement show n3 + n < 3n for all n >= 4 Homework Equations The Attempt at a Solution I.H : n3 + n < n for all n >= 4 3(n3 + n) < 3(3n) then (3n+1) = 3 x 3 n > 3((n3) + n ) by I.H...

Homework Statement A 7.40 cm diameter coil consists of 15 turns of circular copper wire 2.3 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of 7.29×10^−3 T/s . Determine the current in the loop. Express your answer using two significant...

Homework Statement Prove (n choose k) ≤ ((en)/k)^k by induction on k. Homework Equations I can't of anything that's awfully relevant besides the general steps of induction. The Attempt at a Solution So I found it true for the k=1 case which was easy enough. Then assumed true...

Homework Statement I am working on a mathematical induction problem, where I need to prove: (1 - (-7) ^ (k + 2)) / 4Homework Equations (1 - (-7) ^ (k + 1)) / 4 + 2(-7) ^ (k + 1) The Attempt at a Solution So I just need to add the two items in section two above. Now I know I need a common...

I'm having a little bit of difficulty with proofs by induction. I believe I understand the principles behind induction but find that I often get "stuck" in my proof - and I can "see" that its true but am not sure how to get that one step that will finish the proof. When using mathematical...

Homework Statement Prove that 3^n >= 2n+1 for all natural numbers. Homework Equations 3^n >= 2n+1 [is bigger or equal to] The Attempt at a Solution 3*1>=2+1 True for n=1 Assumption: 3^k>=2k+1 3^(k+1)>=2k+3 3^k*3>=2k+3 (2k+1)*3>=2k+3 <---can I just substitute 2k+1...

u_{n} = \sum_{k=1}^{n}\frac{1}{n+\sqrt{k}} Proof that: \frac{n}{n+\sqrt{n}} \leq u_{n} \leq \frac{n}{n+1} Ok, I've been working on that problem for about two hours now and I still don't have a clue how to proof this inequality. I guess it should be done by induction, but I have problems...

Homework Statement Use mathematical induction to prove the following statements are true for n≥1 a) 1^2+3^2+5^2+...+(2n-1)^2= [n(4n-1)]/3 Homework Equations The Attempt at a Solution Attempt at showing for n+1 is true: n[4(n+1-1)]/3+ 2[k+1-1)^2

1 = 1 1 - 2^2 = -(1+2) 1 - 2^2 + 3^2 = (1+2+3) 1^2 - 2^2 + 3^2 - 4^2 = -(1+2+3+4) and so on. I have to prove that this relationship is true for all natural numbers. This is what I did: clearly it is true for 1, 2, 3 and 4. assume true for n odd: 1^2 - 2^2 + 3^2 - 4^2 ... + n^2 = (1 + 2 + +3...

1. Homework Statement [/b] Use mathematical induction to prove the following statements are true for all integers n≥1 1+2+2^2+2^3+...+2^n-1=2^n-1 Attempt at a solution: For n=1 1+2^(1-1)=2^1-1 1=1 ∴ it is true. Let Sn=Sk If it is true for k, it must also be true for...

The question is as follows: Using an induction argument if n > 1 is a natural number then n-1 is a natural number. P(n)=n-1 such that n-1 is a natural number Following the steps: Base case: n=2, P(2)=1 which is a natural number. We fix a natural number n and assume that P(n)=n-1 is...

Homework Statement If a and theta are real numbers such that x + 1/x = 2cos(theta), then: x^n +1/x^n = 2cos(n*theta) Homework Equations x + 1/x = 2cos(theta) The Attempt at a Solution So I was able to show that the statement was true for n=1, but I'm stuck on how to even start...

Ok, so this problem looks like an induction problem to me, so I used that, but I only got as far as the induction hypothesis. The hint says to use the pigeon hole principle. I'm not sure how to use that for this problem.

Homework Statement Prove that n! > n2 for every integer n ≥ 4, whereas n! > n3 for every integer n ≥ 6. Homework Equations See above. The Attempt at a Solution Ok, I am attempting an induction proof, but I seem to be stuck in the following step. In any case, I don't even know if...

Homework Statement Let F: N->N be defined by f(1)=1 and f(2)=2 and f(n+2)=1/2(f(n+1)+f(n)) Use Theorem 1.3 to prove that 1<=f(n)<=2 for all n in N Homework Equations For each n in N let P(n) be a statement about the positive integer n. If a) P(1) is true, and b) for k>1, P(k) is...

When the voltage / frequency is maintained constant in 3 phase Induction motor i.e. flux is maintained constant by changing the voltage and frequency in same proportion, What is the torque proportionality equation. Whether Torque is proportional to Slip X Frequency or Torque is...

Homework Statement I would appreciate some help with the following problem: http://img407.imageshack.us/img407/7647/questionb.jpg Homework Equations This is an equation derived from Biot-Savart law: B= \frac{\mu_0 I}{4 \pi s} \int^{\theta_2}_{\theta_1} cos \theta d \theta =...

Hi, What is the charge on a droplet of paint? Im trying to understand what's going on in electrostatic spray painting - specifically at the spray nozzle (this could also be crop spraying too) My understanding so far is that a paint supply is fed into a grounded nozzle. An electrode...

Homework Statement An iron core with a solenoid coiled around it is in a circuit with a switch and a dc current supply. In front of it, there is a iron ring tied to the ceiling such that it faces the solenoid without touching the circuit. When the switch is turned on what is observed and...

what is mathematical induction? explain with an example.

I'm reading "An Introduction to Mathematical Reasoning," by Peter Eccles. It has some interesting exercises, and right now I'm stuck on this one: "Prove that \[\frac1n\sum_{i=1}^nx_i \geq \left(\prod_{i=1}^nx_i\right)^{1/n}\] for positive integers \(n\) and positive real numbers \(x_i\)."...

:smile: so i was reading an old thread that mentioned the following problem from Apostol's Calculus I I'm not sure if I my solution is correct, so I am posting it here for opinions: The inductive step is correct, i.e. if it can be shown that the theorem holds for n=3, then the theorem is...

Hello this is my first post, please let me know if I'm breaking any rules, I'm still a bit hazy on them. I am in the process of making a permanent magnet induction generator from and old washing machine induction motor. The motor is rated 1725 rmp, 115 volts 6.3 amps at 1/3 horsepower. It is...

Howdy, I am clumsy at best with induction (pretty new to it sadly), and I was wondering if it's proper to prove something false with induction? Every time I've used induction it's always been to prove something true. It may be a dumb question, but I'm beginning to think induction is only for...

Thanks to those who participated in last week's POTW! Here's this week's problem (I'm going to give group theory another shot). ----- Problem: (i) Prove, by induction on $k\geq 1$, that \[\begin{bmatrix}\cos\theta & -\sin\theta\\ \sin\theta & \cos\theta\end{bmatrix}^k =...

Homework Statement Prove that \frac{1}{n}\sum_{i=1}^n x_i\geq {(\prod_{i=1}^n x_i)}^{1/n} for positive integers n and positive real numbers x_i Homework Equations There is also a hint. It states that it does not seem to be possible to prove it directly so you should prove it for n=2^m...

Homework Statement Hi everyone, In my assignment I've been asked to show that 2^n = Ʃ(nCi) i from 0 -> n ie: 2^n = nC0 + nC1 + ... + nCn and I have to do this by induction and then also by a combinatorial argument. Homework Equations Right now I'm just working on the induction part...

Homework Statement this is probably a dumb question, but I'm doing this proof where i have to show two sets are equal, where each set is a union from 1 to n sets. this is pretty easy to show with induction, i think, but I'm used to using induction when i have an infinite amount of things, so...

Prove that f(n) = 4^n + 6n - 1 is divisible by 9 for all positive integers of n. I've proved this by considering that f(k) is divisible by 9, i.e f(k) = 4^k + 6k -1 = 9m where m is some integer. Rearranging to give 4^k = 9m - 4k + 1 and then considering f(k+1) = 4^(k+1) + 6(k+1) - 1 then...

Homework Statement http://imageshack.us/photo/my-images/194/55132039.png/ http://imageshack.us/photo/my-images/194/55132039.png/ How much curret flows trough circuit ABCD when the center of the circuit (O) is distance r from the straight wire? I think these are the relevant equations...

I am interested in a little fun... It has been some time since I have done any set theory, and I am forgetting the symbols and ideas... So, I wanted to construct a strong inductive proof, and get a bit of help with how to concisely write the proof, and how to get TEX here at the forums to...

I'm not sure whether to post here or EE forum, if it is better suited there, please advise/assist in moving it. I'm familiar enough with Induction, though not practiced in the formulae describing it. I recently came into need of an AC generator and thought there has to be some useful...

Homework Statement Prove the binomial theorem by induction. The attempt at a solution http://desmond.imageshack.us/Himg35/scaled.php?server=35&filename=sumu.png&res=landing Hi, running into trouble with this proof and google hasn't helped me. I don't understand the jump here, and as...

I want to get a larger flow rate out of a common 3 speed induction motor desk fan. Without forking out for an off the shelf VFD, I thought perhaps I could build a frequency doubler using a bridge rectifier. Following the circuit from left to right, I'm thinking that I'll feed the 240V...

Hi , i am a high school student ( class 10 ) and after reading about electromagnetic induction iwas thinking about what if u place a wire coil connected to a circuit in the magnetic field / near a generator ? Because electricity is turned of for a fraction of a second there will be great...

Smaller generators are sometimes self-excited, which means the field coils are powered by the current produced by the generator itself. The field coils are connected in series or parallel with the armature winding. When the generator first starts to turn, the small amount of remnant magnetism...

Hello, I have the following recurrence equation $$T(n)=aT(n-1)+bn$$ Using substitution, I have solved it to the following form $$T(n)=a^{n-1}+b \sum_{i=2}^{n}ia^{n-i}$$ Now I am trying to prove my solution is correct using induction, but I'm a bit lost. Any advice on how to conduct this...

Homework Statement "Use strong induction to show that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 2^{0} = 1, 2^{1} = 2, 2^{2}= 4, and so on. [Hint: for the inductive step, separately consider the case where k+1...

Hi, I'm currently taking Discrete Mathematics and I'm working on a mathematical induction problem that's a little different than usual because it has a summation in it. What I basically want to know is did I do parts A and C correctly? Homework Statement Homework Equations The Attempt at a...

I want to now the answer of this question and I think it relates to mathematical induction. The question is: -Suppose is a natural number. In how many ways can we place numbers around a circle such that each number is a divisor of the sum of it's two adjacent numbers? Who can answer this...

I'm a bit confused on the subject of transfinite induction. I've read that it is equivalent to usual induction on the ordinal number ω (presumably a proof of this can be found in a standard book on the subject - any suggestions?) Does anyone have an example of a case in which this isn't true...

Hello! First of all I have like 5 exercises I don't quite understand so will it be a problem if I create 5 new topics in the next 24h? Homework Statement Prove, by using mathematical induction that if x+1 \geq 0 then (1+x)^n \geq 1+nx. Homework Equations The Attempt at a Solution Basic step...

Hello, I am having trouble solving this problem. Maybe I'm just overreacting to it. In my two semesters in discrete math/combinatorics, I've never seen a problem like this (with two summations) and been asked to prove it. Can some one help? [SIZE="4"]\sum^{n}_{i=1} i^3 = \frac{n^2(n+1)^2}{4}...

Homework Statement This is no homework question, i am only trying to clear my concepts. Lets say i have a conducting rod placed vertically. I give it a charge Q. The charge would stay on the outer surface. The charge will distribute equally over the surface. What would happen if i place the...

A bar-shaped magnet is released along the axis of a long tube of copper. Describe the motion of the magnet and the energy exchanges involved. Neglect air resistance.

Hello I am new to this forum and wanted to ask a question on em induction. I know if a current passes through a wire a magnetic field around the wire is produced and can be amplified by having a coil of wire. If that is then placed in a magnetic field (like between a north and south pole...

Dear friends, 3 phase ind motor is overheated and also tripped during operation. The heat over the induction motor is extremely hot. What will be the reason? Is it due to coil damage inside of motor.? Kindly reply, thank you!