Geometric Definition and 790 Threads

Homework Statement Consider the following infinite geometric series: 1 + (2x/3) + (2x/3)^2 + (2x/3)^3 + ... for what values of x does the series converge? Homework Equations i don't know what converge means, i guessed it was for what vlaues does the geometric series is infinite but...

Homework Statement How can I simplify sum from j=0 to infinite of x^(2j) ? Homework Equations The Attempt at a Solution THis is close to the geometric series but I'd have to square each individual term

Homework Statement Describe geometrically the sets of points determined by the relations: a) |z-i|+|z-1| = 2 b) |z-i|=|z+1| c) Re z = |z-2| Homework Equations The Attempt at a Solution I know the answer of a is suppose to be Ellipse with foci at i and 1, major axis 2 and b...

Homework Statement Which of following sets of conditions (A - F), if true, would show that the expressions 1 and 2 above define the same vector C_vec as expressions 3 and 4? 1. The two pairs of expressions give the same length and direction for C_vec. 2. The two pairs of...

i was doing some exercises nut I'm not sure if my answers are correct 1) X~B(5,0.25) i have to find: a) E(x^2) and my answer was 2.5, is this correct? b) P(x(>or=to)4) and my answer was 0.0889, is this correct? 2) X~Geom(1/3) i have to find: a) E(x) my answer is 1/3 b) E(x^2) c)...

Homework Statement 3. The following calculaltion shows how the ratio of e to kT affects the populations of different energy levels. kT is sometimes called the thermal energy; if it is small relative to e, a particle will not be able to access higher energy states. Consider a harmonic...

Homework Statement The common ratio,ratio,r, of a geometric series is given by: r=\frac{5x}{4+x^2} Find all the values of x for which the series converges Homework Equations The Attempt at a Solution For the series to converge |r|<1 so that |\frac{5x}{4+x^2}|<1 this...

Geometric Models: E8, SO(10), Which ansatzs will prove to be right by CERN? 1. Ali H. Chamseddine and Alain Connes , SO(10) …. the spectral action associated with this noncommutative space unifies gravitation with the Standard Model at the unification scale. … Therefore the bare action we...

I'm currently putting together a basic summary of the Lambda-CDM model and I have a slight issue with the fact that the equation to calculate lambda (which includes factors to convert physical units into geometric units) is incorporated into the omega_lambda calculation (which incorporates the...

Hi everyone! So I'm trying to learn more about inequalities and the one I'm starting with is the power means inequality. But it all seems pretty intuitive except how they define the n=0 power mean (i.e. the geometric mean). I read that it's actually the limit as n->0, but I don't see why that's...

T is the projection onto the xy-coordinate plane: T(x,y,z)=(x,y,0) I have to give a geometric description of the kernel and range of T. my geometric description of the kernel: a line along the z-axis. Is this correct? whats the geometric description of the range of T?

let T:R^{3} \rightarrow R^{3} be a linear transformation. how can i figure out a geometric description of the kernel and range of T. What do I have to look at?

Homework Statement Use cos ( n * x) = (z ^ n + z ^ -n)/2 to express cos x + cos 3x + cos 5x + ... + cos([2n -1]x) as a geometric series in terms of z. Hence find this sum in terms of x Homework Equations The Attempt at a Solution (z + z^-1)/2 + (z^3 + z^-3)/2 + ... +...

I've been studying absolute uncertainties and do not understand any of it. If someone can explain it will really help. Especially with uncertainties including diameters and area.

Homework Statement Give a geometric description of the Span {V_{1},V_{2}} for the vectors V_{1} = [8, 2, -6] and V_{2} = [12, 3, -9] Those should be columns but I couldn't figure that out in latex, sorry. 2. The attempt at a solution I have a solution, what I need help with is...

hi this is my first participation in this forum I want aske some quastions what is the paraquantization ? can we devloppe a geometric paraquantization? how can demonstrate that the green anzats is equivalent to tri commutation relation of parastatistical particle

I'm sure many of you guys have seen the videos of a beam of light (namely a laser of some sort) pass through a volume of liquid in which there is a gradient of index of refraction from the bottom of the tank to the top. Think of a sugar solution in which more sugar collects at the bottom and...

Hello all. I wasd beginning to feel at home with vectors and covectors but while trying to fully understand the concepts this query came up._________ Excuse the lack of rigorous definition but I think you will realize what I am aiming at. Take a geometrical vector in a finite...

is it possible to have an virtual OBJECT in image formation?

Homework Statement Let A be an arbitrary vector and e be a unit vector in some fixed direction.Show that A=e(A.e)+e x (A x e) What is the geometrical significance of each of the two terms? Homework Equations The Attempt at a Solution I can show it easily.As the first term (a dot...

For the molecule \textrm{Ni}\left(\textrm{OH}\right)_{2}\textrm{Cl}\left(\textrm{NH}_{3}\right)_{3}, how do you determine the number of geometric and optical isomers? I first drew the molecule with a central \textrm{Cl} bonded to three \textrm{NH}_{3} molecules and a \textrm{Ni}; the...

I tried to obtain refraction of light by sun's gravity by substitution of sun's gravitational field by aether with different speeds of light. I do not get right result. Where I am wrong? For light which travel close to the sun by direct trajectory, I get the following speed of light in...

Homework Statement (infinity)sigma(k = 0) [2(2/6)^k + (-2/10)^k) Homework Equations Geometric Series The Attempt at a Solution I split these up into two geometric series (infinity)sigma(k = 0) [2(1/3)^k] 2 / (1 - 1/3) r = 3 This diverges. (infinity)sigma(k = 0) (-1/5)^k...

This example appears in a set of notes entitled Geometric Algebra. I cannot follow the first half of the example. Is the reasoning incorrect. Thanks. Matheinste.

CASTEP Users?? Hi I am a beginer to castep. I am trying to do some geometric optimisations on various materials. The aim is to get familiar. Does anyone know of any tutorials available online other than the ones available in the tcm group cambridge. I would also like to interact and know...

This is the sequence: 1, 2, 5, 14, 41, 122 1. Is this a geometric series or an arithmetic series? 2. I know the formula is a sub n=[3^(n-1)+1]/2, but how do you get that from a sub n=a sub 1 * r^(n-1), which is the geometric formula for series.

I have a simple geometric proof (first proofs) I can't finish. Looks like this: A________L C________E suppose there's a straight line from l to c and a to e (to make an x) and a midpoint I. It says: Given I is the midpoint of both \overline{AE} and \overline{LC}; AE = LC Prove AI...

Can someone pleas explain to me the geometric interpretation of Torsion? Why it is true is more important. Lol i said manifolds instead of torsion!

Homework Statement a) Show that you can split any transformation into a Translation, Dilation-Rotation, Inversion, and Translation. b) Show using part a) that any straight line or circle is send to a straight line or circle when applying the mobius transformation. Homework Equations...

Homework Statement time till first failure of a chip is to be estimated. 3 such chips were tested, they worked for 30, 34, 33 days without failure. Find MLE of the parameter. The Attempt at a Solution first i want to confirm this: is this geometric distribution?

I've been studying geometric algebra of the form promoted by David Hestenes, but I'm having trouble with the very basics. Most GA books, in fact, all GA books, begin as follows. For two vectors \mathbf{a}\mathbf{b}, they define the symmetrical inner product...

I can't figure this out for the life of me: A geometric series exists with the third term of 8 and the sixth term of 128, what is the geometric series?

question - if the 3rd and 9th term of a geometric series with a positive common ratio are -3 and -192 respectively, determine the value fo the first term, a. I kno we using a_n=a_1r^n-1 From that i got this : -3 = a_1r^2 -192 = a_1r^8 But I don't kno how I can solve for r or...

Consider a function of two variable x,y , is it possible to understand the geometric meaning of the gradient just by looking its definition \nabla f = \frac{\partial f}{\partial x} \hat{x} + \frac{\partial f}{\partial y} \hat{y} I can understand the geometric meaning by directional...

Find the geometric power series for the given function: f(x)=6/(2-x) c=1 I am stumped on this one. I've tried for an hour on this one with no luck. Could someone help?

Hello everyone, I'm trying to solve the following: If n is an integer and n > = 1, find a formula for the expression 2^n - 2^{n-1} + 2^{n-2} - 2^{n-3} + ... + (-1)^{n-1} * 2 + (-1)^n okay this confuses me, because I'm not sure which is the first term and which is the last term... I...

I was wondering if someone could check my work: Find the geometric power series representation of f(x)=ln(1+2x), c=0 I get \\sum_{n=0}^ \\infty2(-2x)^n+1 on -1/2<x<1/2

hello everyone, I'm trying to figure out this geometric progession and I'm checking it with my calculator and I'm definatley not getting what they are getting: I'm trying to find the term after the last term, I found the ratio which is 3/2, now I must multiply that ratio by the last term...

Hello everyone. I'm studying for my exam and I'm reveiwing some problems but this one isn't making sense to me: 11^9(9 choose 0) - 11^8(9 choose 1) + 11^7(9 choose 2) - ... - 11^2(9 choose 7) + 11^1 (9 choose 8) - 11^0 (9 choose 9) answer: (11-1)^9 = 10^9 = 1,000,000,000. work...

Hello everyone I'm studying for my next exam and I screwed up on the geometric progressions and arthm and they are the easiest of them all but I don't know what I'm doing wrong. The first problem on the exam said: Suppose that an arithmetic series has 202 terms. If the first term is 4PI and...

ok, the qn goes like this.. Find the first term and common ration of a geometric progression if the sum to n is given by 6 - 2/(3^(n-1)) I tried solving by making both terms of the eqn having the same denominator by multiplying (3^(n-1)) to the first term 6 and then by taking out the 2...

i know that geometric topology is a field that is connected to knot theory, i wonder what are the similarities between the two subjects, and in what subject in particular they overlap?

I am a second year student in quantum mechanics. I heard in lecture that simultaneous diagonalization of matrices is important in quantum mechanics. I would like to know why is it significant when two matrices can be simultaneous diagonalized, and what is the geometric and physical...

do you have an explanation to why sometimes the general term formula for geometric sequence is not raised to n-1 but to simply n?

can a sequence be arithmatic and geometric?? can a sequence be arithmatic an geometric??

I could use some help with this question: Derive the geometric series representation of 1/(1-x) by finding a0, a1, a2,... such that (1-x)(a0+a1x+a2x^2+a3X^3+...)=1 Thank you.

Hello all, I have attached a matrix. I am trying to work out this matrix will transform a set of co-ordinates (x_1, y_1, z_1) to a new set of co-ordinates (x_2, y_2, z_2) Can anyone give me any hints on how to tackle this problem?

We learned in class how to find the sum of any geometric sequence with the following formula: Let x = Sum Of Geometric Sequence; x = [Take mythical next term - real term]/(ratio - 1); The real term is the first term of the sequence and the mythical next term would be the next term for...

I understand the material this problem is based on very well, but I feel very sad when I read this problem because it makes very little sense to me. I'm hoping it's just me that's confused by it and not everyone else - because in that case I should be able to get help here. Here is the...

What is the difference between structural isomerism and geometric isomerism?? Yea. The thread title explains it.