Geometric Definition and 790 Threads

Hi there, Can anybody help please. How can i find the first term in a geometric progression if i know that the 4th term = 256 and the 8th term = 65536?

I am having a little trouble with some questions on geometric series' For example, Find the values of x for which the following geometric series converge I have done the first one easy enough 2+4x+8x^2+16x^3... r=2x |r|<1 |x|<\frac{1}_{2} \frac{-1}{2} < x < \frac{1}_{2} But then it...

I have an arithmetic series, with the sum of the first n terms to be 610. The 1st, 3rd and 11th terms of this AP is the same as the 3rd, 2nd and 1st term of a geometric series. Find the first term of the geometric series. I have constructed 4 equations from this a_p = a_q r^2 a_p+2d...

Hello folks, I found a lovely little book online called A Geometric Approach to Differential Forms by David Bachman on the LANL arXiv. I've always wanted to learn this subject, and so I did something that would force me to: I've agreed to advise 2 students as they study it in preparation...

Help Geometric Sum Help! Plz Hi here is the question It says a retired hockey star wants to set up a scholarship fund to assist an underpriveleged child who would like to go to a post secondary institution. He wants to ensure that the student will have $6000 per year for 5 years. HOw much...

how can I write f(z)= 1/(c(1+z)) as a geometric series with radius of convergence 1, where c is a complex number?

Recall that every point (x, y) in the plane is described by its radius- vector r = xi + yj. A planar curve [gamma] has the following geometric property: at every point on the curve the radius vector and the tangent intersect at a fixed angle [alpha]. 1. Derive a first order differential...

a couple decides that they will have kids until a girl is born. the outcome of each birth is independent event, and the probability that a girl will be born is 1/2. The birht at which the first girl appears is a geometric distribution. what is the expected family size. ok, so we know that...

Let's say y = x^a and you want to find \int^b_a x^a How would you find this using a geometric progression? Thanks

Hi! My problem sounds as following: In the isoscele triangle \triangle ABC, \angle A = 48 degrees. Bisect the angle \angle A against \overline CB in point T. Determine the \angle ATB for the three possible solutions. I've found two of them, but cannot find the last. The first one is if...

General Relativity is assuming the existence of a metric everywhere, in someway depending directly or not on the repartition of the energy. Must I understand this assumption as equivalent to the existence of a background geometric field ? The satellite Gravity Probe B is actually testing the...

10 years ago i tried (as an artist) to solve the problem of how to translate the 3 dimensional cartesian coordinate onto the 2 dimensional surface with the precise foreshortening. I've only ever figured out 3 formulas for 3 different standpoints... then i gave up. now i recollected my notes, and...

Find a power series for the function centered at c and determine the interval of convergence. c = 0 f(x)=\frac{2}{1-x^2} After some partial fractions work and getting the partials in the form of \frac{a}{1-r} I have \sum x^n + \sum(-x)^n if I factor out the x^n's I get...

Hello friends, does anybody have a soft copy of the following paper. if yes, then please mail it to my email address: aditya_tatu@yahoo.com aditya_tatu@da-iict.org I am not sure whether it is freely available online or not? the details of the paper are: Title : The heat equation...

Is there any geometric figure whose calculation (area, perimeter, ...) involves the terms pi^2 or (pi^2-1) ?

When I use d, I am referring to a partial derivative here. So where w(z)=u(x,y) + iv(x,y), and the derivative of w(z) exists, I have shown that (du/dx)(du/dy) + (dv/dx)(dv/dy) = 0 But I have to give a geometric interpretation of this which is somewhat confusing to me. I am not sure what...

A couple plans to continue having children until they have their first girl. Suppose the probability that a child is a girl is 0.5, the outcome of each birth is an independent event, and the birth at which the first girl appears has a geometric distribution. What is the couple's expected...

I want to understand how the formula for the sum of a geometric sequence is created... This is what I understand so far: A geometric sequence is the sum of a series of numbers, where a term will be multiplied by an amount (the common ratio) to get the next term, and so on... ex...

I'm supposed to prove that in a geometric distribution, the expected value, \mu = \frac{1}{p} without the use of moment generating functions (whatever that is) I start off with the very definition of the expected value. \mu_x = E(x) = \sum x \cdot p \cdot (1-p)^{x-1}...

I am told that |z1-z2| is the distance between two points z1 and z2 in the complex plane. I have to give a geometric argument that a) |z-4i| + |z+4i|=10 represents an ellipse whose foci are (0, and positive or negative 4) b)|z-1|=|z+i| represents the line through the origin whose slope is...

A simple[trivial?] postulate that gives a "Universal Set" and resolves the "set of all sets" paradox[in the geometric sense]: A circle of radius R, is isomorphic to a circle of radius 1/R. [1/R]<--->[R] For any arbitrarily large circle of radius R, there is an exact correspondence with...

Given the probability of flipping a heads with a fair coin is \frac{1}{2}, what is the probability that the first heads occurs on a prime number?

Ok I'm working on my geometric optics homework and this is the last problem and I can't seem to get it right. An 6 astronomical telescope has a 32 cm focal-length objective lens. After looking at stars, an astronomer moves the eyepiece 1.0 cm farther away from the objective to focus on nearer...

Problem 8. Find x & y if the sequence 2y, 2xy, 2, xy/2,...is geometric. Problem 9. Find an arithmeitc sequence none of whose terms are divisible by 2, 3, or 7. Prtoblem 10. Consider two arithmetic sequences: A:3, 14, 25.. B: 2, 9 , 16, ... Write the first five...

First off - id just like to say hello to everyone and I am sorry if this has possibly already been posted - but i looked around to check a bit and didnt see anything of the sort ok i supose i ought to explain what i mean: i am only in a sophomore geometry class(high school) but i have tended...

I am having toruble with my geometric progressions, in that i ahv ebeen given a question where i am given the 7th and 26th terms of a GP. I am required to find the ratio however, which i could do if i had the first term. Usually i can do this as they only give me gps that are one term apart, and...

Hi, any advice out there on an interesting challenge (at least a challenge for me :-)? I am trying to come up with the easiest way to calculate the shortest distance between a single point and an arbitrary line. I want to start with lattitude and longitude coordinates for single point and...

I'm currently a freshman in linear algebra, getting ready for the final, and all has been going well. The algebra's pretty much intuitive for me; I tend to enjoy the abstract theoretical stuff :). Anyway, to my question. My professor has done little to none as far as applying the ideas of...

I have a question that I would like your assistance to see if I have the correct info: In 1990 there were 9.19 million cable TV subscribers. By 2000 the number of subscribers increased to 54.87 million. What is the geometric mean annual increase for the period ? Answer...

Question: A man puts $10 in the bank for his son on each of his birthdays from the first to the twentieth inclusive. If the money accumlates at 3% compound interest, what is the toatl value on the son's twenty-first birthday? My answer is like this: a = 10, r = 1.03, n = 20 Total value = a...

Has anyone ever tried to make prime numbers into some kind of geometric equivalence? Such that prime numbers can be predicted through geometry? I was thinking of a universe beginning with one 3D unit, and evolving from that unit. That all subsequent units would have a relation to the first...

Hi, I have a relatively simple question. In this particular problem in my Math 30 Pure textbook... 10. Here are three levels in a school telephoning tree. Teacher Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 a)At what level are 64 students contacted? ...I really...

I understand that an example of a physical interpretation of the line integral of a scalar function with respect to arc length \int_C f(x,y,z)ds might be the total mass of a wire where f describes the linear density of the wire. But can anybody give an example of a physical or geometric...

Consider 3D geometric algebra. Let all points on a line be given by the parametrization x=tu+y, in which the parameter runs from minus infinity to plus infinity. a. Show that for all points on the line we have x(wedge)u=y(wedge)u. b. Show that the vector d pointing from the...

can anyone explain how commutators act on tri-vectors (in orthonormal conditions)? on bi-vectors i know that it ends up to be a bivector again, but with tri-vectors it vanishes if its lineraly dependent. what about the case if its not linearly dependent, does that mean it remains a...

Just wondering... so the conception is that gravity is not really a "force" but rather the consequence of shortest-path motion through curved geometry. Are there analogues for the other forces? I know gravity is not yet theoretically unified with the other forces. But is there nonetheless some...

I'm having trouble with these type of probles (where a negative log comes up): (All of this is solving without sigma notation) Find the number of terms in these geometric sequences and the sum of the numbers. 11, -22, 44,...,704 I know that a1 = 11, r = -2, and an = 704, so I did...

I'm trying to get an A in honors AlgII/Trig and it is impossible, but I won't give up, so I have a few questions. I'm not sure how to find the first two terms of a sequence (I got a few right, but most wrong and I don't know what's wrong). One of the problems is: a5 = 20; a8 = 4/25. I set...

Can you solve analytically [oo] [pi] (n)1/n n=1 or [oo] [pi] (n!)1/n! n=1 or [oo] [sum] (1/n)n n=1 or [oo] [sum] (1/n!)n! n=1 ?

Given n+1 points in n-dimensional Euclidean space, how many polytopes (generalizations of polygons of n to as few as 2 dimensions) may be defined by the representation of each point as a possible vertex?