Geometric Definition and 790 Threads

Homework Statement The Bank of Utopia offers an interest rate of 100% per annum with various options as to how the interest may be added. A man invests $1000 and considers the following options. Option A - Interest added annually at the end of the year. Option B - Interest of 50% credited...

Homework Statement A 'supa-ball' is dropped from a height of 1 metre onto a level table. It always rises to a height equal to 0.9 of the height from which it was dropped. How far does it travel in total until it stops bouncing? Homework Equations The Attempt at a Solution The...

Homework Statement Evaluate the problem: \sum_{k=1}^\infty \frac{3^{(k-1)}}{4^{(k+1)}} Homework Equations \displaystyle\lim_{n\rightarrow\infty} S_n = \frac{a}{1-r} The Attempt at a Solution I know that the limit of the partial sequence is what i need to help solve this, but can't...

Part c) I'm not quite sure what to do, I've found the det(U) is 2, but no idea what this actually shows to be honest, any help?

Let's say I have a series of 100 coin tosses, heads or tails. In fact (for my actual data) I don't know if subsequent trials are correlated or what the actual probabilities of getting heads or tails are. Nevertheless, I want to fit a geometric distribution, which gives me the distribution of the...

I'm struggling with trying to visualize the vector potential as in the identity: B = ∇⨯A For starters, how does A relate to, say, a uniform magnetic field, which is quite easy to visualize. Then, how about the magnetic field around a bar magnet -- where is A? Any help would be appreciated.

Homework Statement With a series like: pi^(n/2)*cos(n*pi) How am I meant to approach this? Do I use the Squeeze Theorem? Homework Equations The Attempt at a Solution

Homework Statement Write the first 5 terms of the geometric sequence 3, __ , 32x+1, __, __ Homework Equations tn=arn-1 The Attempt at a Solution tn=arn-1 32x+1=3r3-1 r2=32x+1 / 3 r=√32x+1 / √3 I'm stuck

Homework Statement Suppose the sequence (Sn) is defined as: |Sn+1-Sn|<2-n show that this is a cauchy sequence Homework Equations hint: prove the polygon identity such that d(Sn,Sm)≤d(Sn,Sn+1)+d(Sn+1,Sn+2)...+d(Sm-1,Sm) The Attempt at a Solution I have defined Sm and Sn and created the...

Homework Statement A ball is dropped from a 100 feet and has a 90% bounce recovery. How many bounces does it take for the ball to travel 1854.94320091 feet? Homework Equations -None- The Attempt at a Solution I know the ratio is .9 and the 'a one' value is 180, so I plugged those values in...

Homework Statement Different numbers x, y and z are the first three terms of a geometric progression with common ratio r, and also the first, second and fourth terms of an arithmetic progression. a. Find the value of r. b. Find which term of the arithmetic progression will next be equal to...

Homework Statement Find the first term in this geometric sequence that exceeds 500. 2, 4, 8, 16, ... Homework Equations Un = arn-1 The Attempt at a Solution a = 2, r = 2 Un = 2 x 2n-1 > 500 2 x (2n)(2-1) > 500 log22 x log22n + log22-1 > log2500 1 x n + (-1) > log2500 n - 1 >...

Hello, I'm currently working through Hestenes' and Sobczyk's book "Clifford Algebra to Geometric Calculus." It has been slow reading because of the many skipped steps in his derivations (I'm not saying that's a bad thing), but I am rather enjoying GA/GC so far. I work through all of the...

A man gets a credit card and buys something that charges exactly 800 dollars to the card. The APR on the card is 18 % compounded monthly, and the minimum payment is 15 dollars a month. What is the expression for A(n), the balance on the card after n months? (This should be a geometric series)...

Use geometric series to find the Laurent series for f (z) = z / (z - 1)(z - 2) in each annulus (a) Ann(1,0,1) (b) Ann(1,1,∞) Ann(a,r,R) a= center, r=smaller radius, R=larger radius Ann(1,0,1)=D(1,1)\{0} My attempt: f(z)= -1/(z-1) + 2/(z-2) geometric series: Σ[n=0 to inf] z^n - 1/2...

Homework Statement Ʃ(1 to infinity) (2/3)^(3n)Homework Equations For a geometric series, the series converges to a/1-r The Attempt at a Solution I'm really just confused about how to manipulate this so that it has a form of ar^n, especially since it starts at 1 rather than 0. I know that...

Hi! Probably I am just confused, but why for the exact solution of the geometric brownian motion dX_t = \mu X_t dt+\sigma X_t dW_t we have to apply Ito's lemma and manipulate the expression obtained with dlogX_t? Couldn't we directly use the espression dX_t / X_t = dlogX_t in the equation dX_t /...

Hi, I have the following equation: \gamma=\frac{1}{\frac{1}{N}\sum_{n=1}^N|\lambda_n|^{-2}} where lambdas are the eigenvalues of an N-by-N circulant matrix A. I used two properties to bound the above equation...

On this website http://www.albany.edu/~bd445/Eco_466Y/Slides/Infinite_Geometric_Sum,_Proof_Without_Words.pdf there is a "proof without words" of the sum of the infinite geometric series. However, I don't understand what makes the proof valid. In what order were the constructions done etc.? What...

[FONT=arial narrow]Dear friends, I have divided the time into slots of fixed size. And i toss a coin of probability of heads 1/2 in the first slot. In the next slot, i toss a coin of probability of head 1/4, and in the i^th slot i toss a coin of prob of head 1/2^i. I do this until i get a...

Homework Statement A ) A company produces microchips. It has some in storage and produces 34 an hour. After 1 hour it has a total of 3428 microchips i) How many chips will the company have a week later, assuming the production continues 24 hours a day? ii)An order is put in for 13,526...

Now for the proof of convergence/divergence of the geometric series we first deduce the Nth partial sum which is given by: \frac{r(1-r^n)}{1-r} Now for 0<r<1 this become \frac{1}{1-r} which clearly converges by AOL At r>1 it's similarly obvious why it diverges. But at r=1, I'm a bit...

I've spent all day on this problem and am wasting precious time needed for other work - please give any input you can! The question: given two wages, w1 and w2 where w2 > w1... a. the difference between the wages as a proportion of the lower: a = (w2 - w1) / w2 b. the difference between the...

Homework Statement A ball is dropped from a height of 24m and rebounds to a height of 16m. If each time it rebound two-thirds of the previous height, find the total distance traveled by the ball. Homework Equations The Attempt at a Solution I thought this might be a problem...

Find the sum to infinity of the series $1 +2z +3z^2+4z^3+...$

Hi Guys, Long time reader first time poster... This simple question has stumped me all day and I think I've finally cracked it! I'm hoping someone can confirm that, or tell me how wrong I am - either is fine :) One in 1000 cows have a rare genetic disease. The disease is not contagious...

Question: Two faulty machines, M1 and M2, are repeatedly run synchronously in parallel (i.e., both machines execute one run, then both execute a second run, and so on). On each run, M1 fails with probability p1 and M2 with probability p2, all failure events being independent. Let the random...

Question: Two faulty machines, M1 and M2, are repeatedly run synchronously in parallel (i.e., both machines execute one run, then both execute a second run, and so on). On each run, M1 fails with probability p1 and M2 with probability p2, all failure events being independent. Let the random...

Hello, Second term of a geometric series is 48 and the fourth term is 3... Show that one possible value for the common ratio, r, of the series is -1/4 and state the other value. ar=48, ar^3= 3... so ar^3/ar=3/48 which simplifies to r^2 = 1/16, therefore r = 1/4 Can anyone explain where...

Rather than arithmetic ("plus or minus") uncertainties, are there classical (not of Heisenberg uncertainty principle) measurements whose uncertainties otherwise appear as geometric ("times or divided by")?

Homework Statement A large cube of glass has a metal reflector on one face and water on an adjoining face (the figure). A light beam strikes the reflector, as shown. You observe that as you gradually increase the angle of the light beam, if Theta is greater than 58.7 no light enters the water...

I just sent some time dicking around with the MacLaurin expansion of exp(-z2) to derive a series expression for √π, by integrating term-by-term along the real line. I'm not really concerned with wether this is a useful or well-studied expression, I just thought it would be a fun exercise...

Homework Statement A geometric series had first term 54 and 4th term 2. (i) What is the common ratio? (ii) Find the sum to infinity of the series. (iii) After how many terms is the sum of the series greater than 99% of the sum to infinity? Homework Equations N/A The Attempt at a...

Homework Statement Determine if the sequence {an} below converges or diverges. Find the limit of each convergent sequence an = n!/nn Hint: Compare with 1/n . Find the limit of the sequence {an} if it converges. I missed the lesson on factorials, and the book is useless. Sorry...

If our sun is the source of illumination, how can an object be observed from the Earth at full phase? Wouldn't the Earth eclipse the object? So then why can we see a full moon during full phase? Is it because the moon's orbit is inclined wrt to the Earth-Sun orbit? If so then wouldn't this by...

Homework Statement How do you find the median of the geometric distribution? Homework Equations M is median if P(X>=M) >= 1/2 and P(X<=M)>=1/2. The Attempt at a Solution I have found this inequality using the geometric series: (m-1)*log(1-p) >= 1/2

Homework Statement here is the series: \sum^{\infty}_{n=0}x(-15(x^{2}))^{n} Homework Equations The Attempt at a Solution I know that -1<-15x^{2}<1 for convergence (because of geometric series properties) but I run into a problem here: -1/15<x^{2}<1/15 You can't...

Generalizing past the quadropole moment-- geometric understanding of the octopole+ I'm having a bit of trouble articulating my question, but I hope the explanations will help you to understand the source of my confusion: The mono, di, and quadropole moments are all geometrically...

Homework Statement Posted this thread earlier but had mis read the given answer. please disregard older thread as I don't know how to delete it! Write down the condition for the numbers p, q, r to form an arithmetic sequence & geometric progression. Homework Equations \ a_n =...

Homework Statement Problem H-10. We will compute the mean of the geometric distribution. (Note: It's also possible to compute E(X^2) and then Var(X) = E(X^2)−(E(X))^2 by steps similar to these.) (a) Show that E(X) = (k=1 to infinity summation symbol) (k
*q^k−1*
p) where q = 1−p. (b)...

I would like to find a nice formula for \sum_{k=0}^{n - 1}ar^{4k}. I know that \sum_{k=0}^{n - 1}ar^{k} = a\frac{1 - r^n}{1 - r} and was wondering if there was some sort of analogue.

Hi guys, It's been a while since high school, and now I'm faced with a problem I need to solve in a few days (attached). Would someone please help me through that? I would really appreciate support.

[FONT="Arial Black"][SIZE="4"]Problem 1 A flat screen TV is place on a wall in a room. A lens of focal length 50cm is placed between the television and the opposite wall so that a sharp image with one quarter of that of the area of the television is produced on the opposite wall. Answer...

Homework Statement Well, the problem is to find the area of: {(x,y), -(pi/2) <= x <= Pi/2, 1/2< y <=cosx} The Attempt at a Solution Well, I know that for an angle of 60 degrees, the cosine is 1/2. So I guess that the limits of my integral will be from 0 to Pi/3. But I'm getting confused...

Homework Statement Homework Equations a(1-r^[n+1])/(1-r) The Attempt at a Solution So I wrote it as e^(-iNz) [1 + e^(iz) + e^(2iz) + ... + e^(2iNz)] Let r = e^(iz), a=e^(-iNz) a [1 + r + r^2 + ... + r^(2N)] From here I'm not sure what to do. I tried letting n=2N, and...

Just a little help understanding results obtained. I have found the closed form of a sequence, but am a little unsure if there is a right way or can select either way of using the terms to create the explicit formula. I have found the common difference from the terms, which is 1.2, in my...

Homework Statement a) P(X=x)=pq^x,\,x\geq 0 Find the PGF. b) P(X=x)=pq^{|x|},\,x\,\epsilon\,\text{Z} Find the PGF. 2. The attempt at a solution a) G_X(s)=E(s^X)=\displaystyle\sum_{x\geq 0}pq^x s^x=p\displaystyle\sum_{x\geq 0}(qs)^x=\frac{p}{1-qs} b) Not sure about this one... Is it: as...

Let r = √(x^2+y^2+z^2) One can easily show that \nablar= \vec{r}/r. But I'm having a hard time understanding what this means geometrically - who can help? :)

I'm interested in the proper way to give a mathematical definition of a certain geometric property exhibited by certain maps from points to sets. Consider mappings from a n-dimensional space of real numbers P into subsets of an m-dimensional space S of real numbers. For a practical...

I have performed numerous calculations of dot products throughout my math courses, but I think I lack a fundamental understanding of what it actually means, beyond the abstract way I have been taught to deal with them. I know the definitions (it's the inner product, or the projection of A on to...