Geometric Definition and 813 Threads

Here is a question that I have a problem with, It doesn't seem to have a solution: An increasing sequence that is made of 4 positive numbers, The first three of it are arithmetic series. and the last three are geometric series. The last number minus the first number is equal to 30. Find the sum...

I'm a little confused on geometric series. My book says that a geometric series is a series of the type: n=1 to ∞, ∑arn-1 If r<1 the series converges to a/(1-r), otherwise the series diverges. So let's say we have a series: n=1 to ∞, ∑An, with An = 1/2n An can be re-written as (1/2)n, which...

My professor states that "A matrix is diagonalizable if and only if the sum of the geometric multiplicities of the eigen values equals the size of the matrix". I have to prove this and proofs are my biggest weakness; but, I understand that geometric multiplicites means the dimensions of the...

Is there a simple geometric interpretation of the Einstein tensor ? I know about its algebraic definitions ( i.e. via contraction of Riemann's double dual, as a combination of Ricci tensor and Ricci scalar etc etc ), but I am finding it hard to actually understand it geometrically...

Homework Statement \lim_{n \to \infty}\frac{(-1)^{n+1} \cdot n^2}{n^2+1} Homework Equations \lim_{n \to \infty}a_n \neq 0 \rightarrow S \ is \ divergent The Attempt at a Solution I tried L'Hopital's rule, but I could not figure out how to find the limit of that pesky (-1)^{n+1}. Edit: This...

Homework Statement Complete the proof that ln (1+x) equals its Maclaurin series for -1< x ≤ 1 in the following steps. Use the geometric series to write down the powe series representation for 1/ (1+x) , |x| < 1 This is the part (b) of the question where in part (a)I proved that ln (1+x)...

The geometric annual annuity runs for a period of 45 years which starts now. • The first payment at the end of the first year from now amounts to R2 000. • The growth rate of the annual payments equals 7% per year during the first 30 years (of the period of 45 years). • The growth rate of the...

Homework Statement As shown in the diagram (attached), ABDF is a rhombus, ACE is an equilateral triangle, and AB  AC . Find ABC through geometric reasoning (a scale diagram will gain no credit). 2. See drawing (picture attached) The Attempt at a Solution If I make angle ABC = x then BCA is...

*I am struggling with arithmetic and geometric sequences. if the 4th term is m-8, 6th term 8m+3 and 8th term is 10m-5 Calculate the 1st and 5th term Which term will have a value of -70The 4th term of geometric sequence is -16 and the 6th term is -64. Calculate the 3rd and 5th terms. thank you...

z1,z2,z3 are distinct complex numbers, prove that they are the vertices of an equilateral triangle if and only if the following relation is satisfied: z1^2+z2^2+z3^2=z1.z2+z2.z3+z3.z1 so i shall show that |z1-z2|=|z1-z3|=|z2-z3|but i do not know how to start.

I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... I am currently focussed on Chapter 3: Advanced Calculus ... and in particular I am studying Section 3.3 Geometric Sets and Subspaces of T_p ( \mathbb{R}^n ) ... I need help with a...

I'm learning geometric algebra. There is a very simple statement which I think is wrong. But it must be right, because all the experts say so. Arrg! The only properties used are 1a = a1 = a aa = 1 if b<>a then ab = -baTheir claim is that abcdabcd = -1. Let's see: aa = 1 abab = -abba =...

what is the rationale of multiplying "r" to the second line of series? why does cancelling those terms give us a VALID, sound, logical answer? please help. here's a video of the procedure

When a test charge is stationary, it generates an E field with zero curl. When it moves, it generates a circulating magnetic field B...( as well as the E field.) Is there a geometric reason for this? How does motion alone generate a circulating field B? Can we call this change a...

So there was this question: Which sample demonstrates particles arranged in a regular geometric pattern? A. CO2(g) B. CO2(s) C. CO2(l) D. CO2(aq) E. None of the above I chose E because I thought that covalent molecules, when solid, would be arranged in a random pattern, especially since this...

If the cross product in ℝ3 is defined as the area of the parallelogram determined by the constituent vectors joined at the tail, how does one go about proving this product to distribute over vector addition? I've attached a drawing showing cyan x yellow, cyan x magenta, and cyan x (magenta +...

Homework Statement The sum of first three numbers of the arithmetic sequence is 54. If you subtract 3 from the first one, leave the second one unchanged and add 12 to the third one you get the first three numbers of the geometric sequence of the form ##ar + ar^2 + ar^3 + ... ar^n ## Find r...

Homework Statement hello this question is discussed in 2009 but it is closed now If you invest £1000 on the first day of each year, and interest is paid at 5% on your balance at the end of each year, how much money do you have after 25 years? Homework Equations ## S_N=\sum_{n=0}^{N-1} Ar^n##...

Homework Statement Let X∼Geometric(p). Using Markov's inequality find an upper bound for P(X≥a), for a positive integer a. Compare the upper bound with the real value of P(X≥a). Then, using Chebyshev's inequality, find an upper bound for P(|X - EX| ≥ b). Homework Equations P(X≥a) ≤ Ex / a...

Hi! If I have a sequence that its first 4 terms are: 30, -31, +32, -32 The pattern is geometric sequence but has alternating signs.. How can I find its sum .. I know it is composed of 2 sequences .. However, when I try to separate the 2 sequences .. I get them of different "lengths" In...

While I'm fairly sure this question is pretty straight forward, I can't remember why (ii) is not considered a geometric isomer. (The answer is (c)) http://imgur.com/ObccNpv Looking at ii I would have thought it to be trans-pent-2-ene due to the ethyl and methyl group either side of the double...

Homework Statement hello i have a question to this solved problem in the book " Mathematical Methods for Physics and Engineering Third Edition K. F. RILEY, M. P. HOBSON and S.J. BENCE " page 118 Consider a ball that drops from a height of 27 m and on each bounce retains only a third of its...

Hi, I have been wanting to do this for a while but not too sure how to go about it. I have the following geometric algebra \lbrace\mathbf{e}_{i}\rbrace_{i=0}^{3} which satisfy the following relations: \mathbf{e}_{i}\mathbf{e}_{j}=-\mathbf{e}_{j}\mathbf{e}_{i} and...

Homework Statement A ray travels as shown in the image attached below. In this case, Fermat's principle may be written as ##A =\frac{n(1+ay)}{\sqrt{1+(y')^2}}## Where y' is dy/dx, n is the index of refraction and A is a real constant. The trajectory of a ray of light is given by ##y =...

Homework Statement I was browsing online and stumbled upon someone's explanation as to why 1 -2 +3 -4 + 5... towards infinity= 1/4. His explanation didn't make sense to me. He starts with a geometric series, takes a derivative, and plugs in for x = -1, and gets a finite value of 1 -2 + 3 - 4...

Hi everyone, I am generally familiar with convergent series. However, in one economics paper (Becker&Tomes 1979), I found the following that confuses me:$$\sum_{j=0}^{k} \beta^{j} h^{k-j} = \beta^{k}(k+1)\quad \text{if} \quad\beta =h$$ however, $$\sum_{j=0}^{k} \beta^{j} j^{k-j} =...

this starts as a calculus question, but springs into where i can get help with david bachman's A GEOMETRIC APPROACH TO DIFFERENTIAL FORMS second edition. looking at paul's notes cheat sheets http://tutorial.math.lamar.edu/cheat_table.aspx we have## \int \frac{1}{\sqrt{a^{2}-x^{2}}} =...

Homework Statement If three number are chosen randomly from the set ##{1,3,3^2,...3^n}## without replacement, then the probability that they form an increasing geometric progression is? (a) 3/2n if n is odd (b) 3/2n if n is even (c)3n/2(n² -1) if n is even...

guys i want a book where i can find questions on geometric optics especially for questions based on locating position of mirror by ray diagram when only object and image are given? I have already found 2 questions in I.E. Irodov but i want more so please suggest other books..... thnx

Show that all point inside of an circle is his center. Consider the metric $d_p(n+m)=|n-m|_p.$

a concave mirror of 5cm radius of curvature whose circular ring has a radius of 4cm is blackened except for a narrow strip round the edge. A beam of light parallel to the principal axis falls on the mirror. Find the distance between the centre of curvature of mirror and the point at which light...

Is correct to say that two vectors , three vectors or n vectors as a common point of origin form a tensor ? What is the correct geometric representation of a tensor ? The doubt arises from the fact that in books on the subject , in general there is no geometric representation. Sometimes appears...

x+x^2+x^3+x^4... = 14 Find x Could someone please provide an explanation. Thank you

x+x^2+x^3+x^4... = 14 Find x Could someone please provide an explanation on how to solve this?

F = k{R}^{4} The flux F is volume of blood per unit time. This is proportional to the 4th power of the radius R of the blood vessel. All I am given is 3% increase in radius will affect blood flow how. I am to find whether is decreases or increase blood flow and by what percent...

In order to construct a geometric series we do the following: chose a number a such that a does not equal 0 and a second number r that is between (-1,1). We call r the ration because it is the ratio, the progression of each term to its predecessor. We have An=a+ar+ar^2+ar^3...ar^n We multiply...

I am currently taking calculus 3 and I am a little confused about the concept of double and triple integrals. Analytically, it's a breeze. I understand how to set limits, do all calculations, etc. What my question is, when I get an answer, what does the answer "mean"? For example, in this...

I been googling videos and notes regarding the sketching of geometric figures, such as: planes, solids, 3rd/ 2d geometric shapes. Could not find decent resources. The reason i ask is that I am having a hard time picturing certain problems with my mediocre drawing skills and I also tutor so it...

The normal algebric probability is easy to understand but I find the geometric probabilities less understandable. Can you please help me with a few problem related to this area of probability so that I can understand it better. Here are my problems, 1. Two persons A and B agree to meet at a...

Homework Statement The profiled steel I above is topped by a " profiled C ". Determine the moments of inertia of the structure composed by the axes central x and y through its geometric center C. Picture representing the problem: Homework Equations Profiled C and I information: The Attempt...

Homework Statement 2^32 – (2 + 1) (2^2 – 1) (2^4+1) (2^8+1) (2^16+1)} is equal to Homework EquationsThe Attempt at a Solution Solved it by opening the bracket Answer: 2^31 + 2^24 + 2^ 18 - 2^7 + 2 Option' are 0 1 2 2^16 None of the options matched... Is there a mistake in question statement...

Homework Statement Alfred puts 985 USD on his bank account every time he has a birthday. Alfred just turned 48. He started to save money when he turned 35 (including 35th birthday). How much money is there on his savings-account if the interest-rate was 3.7% every year and that he had no money...

Homework Statement The question is to specify all forces and constraints that are applied in a system of a two-seat merry go round model in terms of the generalised coordinates - and their type (e.g. geometric, kinetic). http://i.imgur.com/FQ7PJyg.png The system is modeled as central...

In a geometric mean equation, say 2 x 8 = 16, or a x b = c, what are the words we would use to describe the numbers or terms? Specifically, if you know 'a' and 'c', what do you call 'b'? For example, in a normal multiplication, a x b = c, 'a' is the multiplicand, 'b' is the multiplier, and 'c'...

The question is: Determine the Taylor series of f(x) at x=c(≠B) using geometric series f(x)=A/(x-B)4 My attempt to the solution is: 4√f(x) = 4√A/((x-c)-B = (4√A/B) * 1/(((x-c)/B)-1) = (4√A/-B) * 1/(1-((x-c)/B)) using geometric series : 4√f(x) = (4√A/-B) Σ((x-c)/B)n f(x)= A/B4 *...

Homework Statement Suppose x-2,x and x+6, where x is an integer, are consecutive terms in a geometric sequence S Determine x Homework Equations r=x/(x-2)=(x+6)/x The Attempt at a Solution x/(x-2)=(x+6)/x cross multiply x(x)=(x-2)(x+6) x^2=x^2+4x-12 x^2-x^2+4x-12/4=0 4x=12 x=3

Homework Statement A fish 2cm long is floating in a spherical glass fishtank with radius 20cm. The glass is 0.8cm thick and has index of refraction n=1.56. The index of refraction of water is 1.33. Find the apparent position and length of the fish. Homework EquationsThe Attempt at a Solution I...

Hi. Choose 3 random points M,N,P on sides of an equilateral triangle ABC . What's the probability that area of MNP is greater than or equal to half of area of ABC? What's the probability if points are chosen inside ABC?

If QM is a statistical model to approximate something underlying space time we don't quite understand yet, and there is a complex geometry underlying space time, is it possible to find other ways to simplify molecular optimizations and electron interactions in computational chemistry using...

Homework Statement How does a geometric series have a sum, or converge? Homework Equations Sum of Geometric Series = ##\frac {a} {1-r}## If r ≥ ±1, the series diverges. If -1 < r < 1, the series converges. The Attempt at a Solution How exactly does a infinite geometric series have a sum...