Geometric Definition and 813 Threads

Homework Statement Determine whether the serie is convergent or divergent , if it is convergent find its sum. Ʃ∞n=1 (1 + 2n )/ 3n Homework Equations Ʃa(r)n-1 = a / (1-r) r < 1 is converging or if r > 1 diverging The Attempt at a Solution Well I can see its a geometric series...

Homework Statement If a,b,c, are at the same time fifth, seventh and thirty seventh member of arithmetic and geometric progression then a^{b-c}b^{c-a}c^{a-b} is: The Attempt at a Solution I tried solving system of equations but i have four unknown. I was able to reduce it to on unknown...

I'm not a geometer, so I beg for indulgence on the below: In a modern geometrical description of electromagnetism (either in flat or in curved space-time*), I see at least 3 (or 4) (fiber) bundles over the 4D space-time taken to be the base space: * 1 the cotangent bundle and the bundle of...

after finding out what geometric multiplicity was, I was surprised to notice that in every question I'd done it was always 1. So I'm trying to prove an example with g.m. > 1 to see why it works. I've found a matrix which definitely has an eigenvalue with g.m. = 2. I've checked everything with...

Could someone please explain to me (with an example if possible) what is the Geometric Multiplicity of Eigenvalues? I cannot understand it from what I have read on the web till now. Thanks in advance.

\sum^{\infty}_{k=4} \frac{1}{5^{k}} ar^n=a/(1-r) Here is what I did: a=5 r=1/625 (1/5)/(1-1/625)=(1/5)/(624/625)=625/3120=125/624 The Answer is 1/500 Where am I going wrong?

Homework Statement The sum S n of the first n terms of a geometric sequence whose nth term is u n is given by 7n-an / 7n Where a > 0 Find an expression for un Find the first term and the common ratio of the sequence Consider the sum to infinity of the sequence Determine...

Homework Statement This problem is taken directly out of a textbook. "The first three terms of a geometric sequence are 1,2, and 4. Susanna said the 8th term of this sequence is 128. Paul said the 8th term is 29. Explain how the students found their answers. Why could these both be...

Homework Statement Calculate the theoretical yield of the isomers from your data. Note: Find the limiting reagent. List of Masses I obtained during lab: Maleic Anhydride (C4H2O3): 5.05g, molar mass=98.1g/mol Impure Fumaric Acid: 2.28g Pure Fumaric Acid(trans-C4H4O4): 1.45g Pure Maleic...

Homework Statement An object is placed 400 mm in front of a convex lens of focal length 80 mm. Find the position of the image formed. State the nature of this image. A second convex lens of magnifying power X8 is placed 125 mm behind the first convex lens. What is the focal length of...

Homework Statement The question is attachedk Homework Equations Sn = n/2[2a+(n-1)d] Sn = (a x (1-r^n))/1-r The Attempt at a Solution I already found the general formulas: Tortoise: Sn = n/2(40) Hare: Sn = (1000 x [1-0.5^n])/0.5 And I know that there tortoise will finish the...

Homework Statement refer to question image Homework Equations refer to question image againThe Attempt at a Solution refer to working out image This is my brothers maths homework. He normally doesn't use online methods to request help and this is his first time.

I'm trying to find a way to simplify a complicated proof. The worst step of the proof involves a product of five 4×4 matrices. I'm hoping, perhaps naively, that if I could understand why the result of this operation is so simple, I may be able to explain the proof to others without actually...

Let $X\subset \mathbb{A}^n$ be an affine variety, let $I(X)=\{f\in k[X_1,\ldots,X_n]:f(P)=0,\ \forall P \in X\}$. We consider the ring $$A=k[a_1,\ldots,a_n]=\frac{k[X_1,\ldots,X_n]}{I(X)}$$ where $a_i=X_i \mod I(X)$.Noether normalization says that there are algebraically indipendent linear forms...

So let ℝ^{n}_{a}={(a,v) : a \in ℝ^{n}, v \in ℝ^{n}} so any geometric tangent vector, which is an element of ℝ^{n}_{a} yields a map Dv|af = Dvf(a) = \frac{d}{dt}|_{t=0}f(a+tv) this operation is linear over ℝ and satisfies the product rule Dv|a(fg) = f(a)Dvg + g(a)Dvf if v|a =...

I am looking for a way to sum some numbers. I understand that if I want to sum pi, I can use the geometric series: \sum\limits_{i=0}^N p^{i} = \frac{1-p^{N+1}}{1-p} But can anyone help me with what to do when I need: \sum\limits_{i=0}^N p^{i} q^{ti} where t is just a constant...

Here is the question: Here is a link to the question: Geometric sequence question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I have the following summation where a is a positive constant and can be > 1 $$ \sum_{k=2}^{n}a^{n-k} $$ I am trying to find a general formula for this summation, which turns out to be a geometric series with a as the common ratio. I have worked out the following: $$ \sum_{k=2}^{n}a^{n-k} =...

Hi everyone, long time lurker first time poster. There's been a some debate here on AdS/CFT and I can't resolve the facts of the matter. I have read Maldacena's large-N paper but of course there is no mention of AdS/CFT in there. The reason I'm posting is because I was hoping someone could...

I had a serious problem when I read my first book on calculus-based physics when I came to the center of mass & moment of inertia sections of my books. I really freaked myself out over the fact that even restricting ourselves to the most common & ideal geometric objects the list of things you'd...

Hey! I have this: 2(√(1-a^2 ))+ 2a How to determine the maximum value of this? I think good for this is Inequality of arithmetic and geometric means, but I don't know how use this, because I don't calculate with this yet. So, have you got any ideas? Poor Czech Numeriprimi... If you...

Good Day, My friends and I are stuck on solving the last part of the attached problem. The solution is 2^[(n^2 + n)/2] - 1. Can anyone help us with solving this? Thanks & Regards, Nicodemus

At time 2:20, the woman says, "Using trigonometry, we know that this angle is the same as this angle." Which trigonometry or geometry property is she referring to that is needed in order to determine those two angles are equal? Is there a name for it? I don't have a geometry book, but I am...

Orthogonal set -- Geometric interpretation Hello, If we have two vectors u,v then in an inner product space, they are said to be orthogonal if <u,v>=0. Well, orthogonal means perpendicular in Euclidean space, i.e. 90 degrees. How <u,v> becomes zero. Secondly, if I have three vectors...

Homework Statement The problem is Q2 in the attached Homework Equations The Attempt at a Solution I am trying to determine the rigion of parameters for each number of crosses,where x and y are the distances of the center of cross from the closest line respectively,and θ is the acute angle.I...

I really need help with this problem. Give me at least a hint on how to solve it. You are standing in front of a lens that projects an image of you onto a wall 2.00m on the other side of the lens. This image is three times your height. A) How far are you from the lens? B) What is...

Homework Statement Ʃ(A-i)/(N+1-i) sum of i=1 to N Homework Equations How do I solve this series for all 0<N<A cases. This series is the sum of N geometric variables of changing probability. I'd appreciate any help

Homework Statement A lever is orientated along the y direction in a Cartesian coordinate system. The length of the lever is 0.5m and one end of it is at the origin of the coordinate system. A (3i-5j)N force applied to the other end of the lever. Calculate the Torque produced by the force...

The Problem: Let a(n) = (n^2)/(2^n) Prove that if n>=3, then: (a(n+1))/(a(n)) <= 8/9 By using this inequality for n = 3,4,5,..., prove that: a(n+3) <= ((8/9)^n)(a(3)) Using the comparison test and results concerning the convergence of the geometric series, show that: The...

$a,b,c$ are any three positive numbers such that $a+b+c=1$. Prove that $$ab^2c^3 \leq \frac{1}{432}$$

Homework Statement How many terms are in each sequence? 12, 4, 4/3, ..., 4/729 Homework Equations The Attempt at a Solution using tn=t1(r)(n-1) ? I am lost

Homework Statement I should know this (it's been a few years) but can't seem to get the answer for: Ʃ (from i = 0 to n) 0.5-i the answer is apparently 2n+1-1 / 2 - 1 how do I go about getting this? Homework Equations I tried Ʃn-1k=0ark = a* 1-rn / 1 - r with no luck The Attempt at a...

Geometric Tolerances - Do standards for defining "general geometric tolerances" exist For example, if I want to define non-geometric tolerances for the whole part, I just write what type of IT it is. For instance, IT8. And then the manufacturer just looks at the chart to know the tolerances he...

Homework Statement I am trying to prove how \(g''(r)=\sum\limits_{k=2}^\infty ak(k-1)r^{k-2}=0+0+2a+6ar+\cdots=\dfrac{2a}{(1-r)^3}=2a(1-r)^{-3}\). I don't know what I am doing wrong and am at my wits end. The Attempt at a Solution (The index of the summation is always k=2 to infinity)...

Hello, Typically the area of a parallelogram if give by A=b*h The det(M) =ad-bc, where m=2x2 matrix. How they are related? -- Shounak

Hi. I'm currently tutoring this student with High school math, and I'm completely stumped on this question that he was asked on his test. I'm hoping the community can help me help my student! Homework Statement The student was presented with two sums of a geometric sequence (eg, Sum of...

Homework Statement We roll a fair die until we get a three or a four. Z denotes the number of rolls needed. What is the probability that Z >= 3? (replacement assumed) Homework Equations Geometric distribution seems logical here? The Attempt at a Solution Let p(A) = p(getting a...

Hello, can anyone suggest a geometric interpretation of the metric tensor? I am also interested to know how we could "derive" the metric tensor (i.e. the matrix <ai,aj>) from some geometric considerations that we impose.

Homework Statement Suppose that X_1, X_2, ... are identical and independently distributed with F_x1(x) = exp(x)/(1+exp(x)) for -infinity < x < infinity Suppose that N independent of X_i has geometric density f_N (n) = P(N=n) = p(1-p)^(n-1) for n =1,2,3,... and 0<p<1 Let Z = max{X_1...

Homework Statement A certain lens focuses light from an object 2.90m away as an image 46.9cm on the other side of the lens. 1. What type of lens is it? (Converging or Diverging?) 2. What is the focal length? 3. Is the image real or virtual? Homework Equations 1/di + 1/do = 1/f...

Homework Statement \sum_{n=1}^{\infty} \frac{1}{2^n} Homework Equations The Attempt at a Solution Could I some how manipulate this to fit a geometric series, so that I may instead use the geometric series test?

Is it true that geometric progressions are \leq arithmetic?

Homework Statement 14 Ʃ 2(4/3)^n n=1 Homework Equations Sn=a(1-r^n)/(1-r) The Attempt at a Solution 2(1-[4^14]/[3^14])/(-1/3)=330.74 However, the answer sheet gives ~441 as the answer, and I confirmed it by doing it by hand. Why is the equation not working? What's wrong?

I was curious if anyone here ever studied Geometric Algebra? It seems not so mainstream and fairly new and I feel intrigued by the subject but I don't want to get in over my head. Just browsing through the table of contents of some books has a lot of unfamiliar terms to me. Here was a...

Homework Statement 1. Prove that 1111111...65 times is not a prime number. 2. If a,b,c,d are in GP , then (a2+b2+c2)(b2+c2+d2) is : (a) (ab+ac+bc)2 (b) (ac+cd+ad)2 (c) (ab+bc+cd)2 (d) None of the above Homework Equations Formulas of GP : 1.Sn = a(1-rn)/(1-r) 2.a,b,c in GP...

Homework Statement Given the nonzero vector a ε ℝ3, a\dot{}x = b ε ℝ, and a × x = c ε ℝ3, can you determine the vector x ε ℝ3? If so, give a geometric construction for x. Homework Equations a\dot{}x = ||a||||x||cos\Theta The Attempt at a Solution I'm not really certain what it is...

Homework Statement I've come across the type of sum in several places/problems but seem to be making no progress in trying to simplifying it further. We have a finite series of some exponential function. \sum_{n=0}^{N}e^{-na} Where a is some constant, a quantum of energy or a...

Homework Statement Determine whether the series is convergent or divergent. Find the sum if possible Ʃ 1+2^n / 3^n n=1 -> infinity Homework Equations a/1-r The Attempt at a Solution I split it up so that the equation is now: Ʃ (1/3^n) + (2/3)^n n=1 -> infinity Ʃ (1/3^n)...

Consider a circle of diameter d. Inscribe a triangle within the circle so that the triangle has hypotenuse d. Prove that this triangle is always right angled. If we define the 3 points on the circumference of the circle that define the triangle as A B and C such that |AC| = d then we...

Hi guys I have a problem to solve, I'd like to find the minimum distance between a point and a geometric locus described in closed form, for example the intersection of two circles: p= point coordinate p1= center coordinate circle 1 p2=center coordinate circle 2 r1=radius of circle 1...