Divergent Definition and 185 Threads

It is well known that the below series are divergent $1 - 1 + 1 - 1 + \cdots $ $1 - 2 + 3 - 4 + \cdots $ $1 + 2 + 3 + \cdots $ But after i watched a video in youtube for the channel " Numberphile " they proved that the first is equal to 1/2 , 1/4 and the last one is -1/12 ! The way to...

Homework Statement Determine whether the sequence is convergent or divergent Homework Equations an = {nn / n! } The Attempt at a Solution an = ( n . n. n ... n ) / 1 . 2 . 3 ... n ) ⇒ an =n [ ( n . n. n ... n ) / 1 . 2 . 3 ... n ) ] ⇒ as n → ∞ , an → ∞ This is further confirmed by...

Hello everyone! My question is: Where is sum of divergent series and divergent integrals used in physics? What it all means? Where can I find examples of divergent integrals? Is there a book of problems for physicists? I am mathematician. I developed a method for summing divergent series...

Hi, I hope that, given I've sourced what I can, you may be able to help? I'm Currently working on a lab report for my Aeroengines unit based on Convergent-Divergent nozzle (http://imgur.com/HQML2Au). From the drawing, I have been provided D1, D2, D3, D4, T1, T2, T3, T4, P1, P2, P3, Velocity...

Homework Statement Is the sequence {(n!)/(n^n)} convergent or divergent. If it is convergent, find its limit. Homework Equations Usually with sequences, you just take the limit and if the limit isn't infinity, it converges... That doesn't really work here. I know I'm supposed to write out the...

Homework Statement 1+\dfrac{2^2}{2!}+\dfrac{3^2}{3!}... \infty The Attempt at a Solution t_n = \dfrac{n^2}{n!} \\ \dfrac{n}{(n-1)(n-2)...1} I tried applying the Ratio Test but couldn't find another function which would give me a finite limit when divided by that function.

Determine whether the integral is convergent or divergent. Evaluate those that are convergent. $\int_{0}^{9} \ \frac{1}{\sqrt[3]{x-1}},dx$ $\int_{-\infty}^{\infty} \ \cos\left({\pi t}\right),dt$ how do i determine whether it's conver/diver?

Homework Statement Which of the series, diverge or converge ∑ 5^n/(4^n +3 ) Homework Equations The Attempt at a Solution Taking the limit as n→∞ we have (5^n ln 5)/ (4^n ln 4) , my question is here how does it become like this, which part am I missing here?

Hello, The point of this thread is to find the mathematical error in summing divergent series. For example the series: 1+2+4+8+16+32+64+...+... (doubling the numbers, or alternatively: increasing powers of 2). I've seen the argument that you multiply the series by 1, then substitute (2-1)...

Determine if the positive term series is convergent or divergent $$ \sum^{\infty}_{n = 1} \frac{n + cosn}{n^3 + 1}$$ can't I just ignore the cosn and look at it like this: $$\sum^{\infty}_{n = 1} (-1)^n \frac{n}{n^3 + 1}$$ Then can't I just look at it as n--> $$\infty$$ and see that I end up...

Homework Statement Prove that the series diverges: \sum_{i=1}^{\infty}\sqrt{n+1}-\sqrt{n} The Attempt at a Solution I'm trying to use the comparison test, but I don't know what to compare it to. All I have done so far is change the terms to be in fraction form...

Homework Statement Is the following convergent or divergent? ln(2(n+1))-ln(2n) Homework Equations comparison test The Attempt at a Solution I put it into the form ln(1+(1/n)), but I don't understand what to use as Bn for the comparison test. (which is what wolfram alpha uses)

Homework Statement Problem is attached in this post. Homework Equations Problem is attached in this post. The Attempt at a Solution I know how to find the sum of this series, but I don't know what method to use in order to prove that this series converges. Also I don't understand how I'm...

How can I tell if the following series is Divergent or Convergent: ∑( e^(6pi*n) sin^2(4pi*n) ) the sum limits are from -infinity to infinity

Homework Statement Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. ∫ from negative infinity to infinity of (x^8*e^-x^9) The Attempt at a Solution The answer is diverged to infinity. But I got that by guessing. Can someone explain to me why...

Homework Statement The problem is attached in this post. Homework Equations The problem is attached in this post. The Attempt at a Solution Lim t -> ∞ ∫ dx/xlnx from 1 to t u-substitution: u=lnx du=1/x dx Lim t -> ∞ ∫ 1/u du Lim t -> ∞ ln u Lim t -> ∞ ln(lnx) from 1 to t Lim t -> ∞...

Homework Statement Please look over my work and tell me if I did something wrong. Suppose Bn is a divergent sequence with the limit +∞, and c is a constant. Prove: lim cBn -> ∞ = +∞ for c > 0 Homework Equations N/A The Attempt at a Solution lim Bn -> ∞ = means that for some value K >...

Homework Statement As a part of Method of Frobenius, I am encountered with the following problems: Evaluate the following limits: Q1. \stackrel{limit}{_{x→0}}\frac{1-2x}{x} Q2. \stackrel{limit}{_{x→0}}\frac{x-1}{x} Q3. \stackrel{limit}{_{x→0}}\frac{1-2x}{x}+\frac{x-1}{x} In context of the...

Homework Statement Ʃ ne(-n2) Homework Equations The Attempt at a Solution I used the ratio test and wanted to know if the way I did it is correct or not |a(n+1) / a(n)| n+1 (e(-n2 -2n-1)) / n e(-n2) Now e-n^2 cancels and we get limn→∞ n+1/n * 1/(e2n)(e) After you take the limits you get...

hey pf! so if i have a vector field \vec{V} and i know \nabla \cdot \vec{V}=0 would i be able to express \vec{V} in the following manner: \vec{V}= \nabla \times \vec{f} for some \vec{f}since we know this automatically satisfies the divergent free requirement? if not, what must be...

Homework Statement Using a proof by cases, show that (-1)^n * (n/(n+1)) is divergent Homework Equations A sequence a_n is said to be convergent if For every real number ε > 0, there exists a natural number N such that for all n > N, |a_n − L| < ε. The Attempt at a Solution Tried...

Homework Statement Prove harmonic series is divergent by comparing it with this series. ##\frac{1}{1}+\frac{1}{2}+(\frac{1}{4}+\frac{1}{4})+(...)## The Attempt at a Solution Clearly every term in harmonic series is equal or larger than the term in the second series ##n \geq 1##, hence like...

Magnet Phenomenon: The "divergent" region of a ring magnet Here's a puzzler: I have a NdFeB ring magnet, 1.75" outer diameter x 1.375" inner diameter x 0.25" thick, N40 grade. It is axially magnetized so that the north pole is toward one face and the south pole is toward the opposite face. The...

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

Hi all, is there any way to find what the largest value of n is such that $$\sum_{k=1}^\infty\frac{1}{k^n}$$ is divergent? I don't need an answer, I need an approach to the problem.

Homework Statement ∞ Ʃ n / 2^n n=1 Homework Equations ratio test lim |a(n+1) / a(n)| n->∞ The Attempt at a Solution I have the answer and the steps its just there's one part I am confused on, first I just apply n+1 to all my n terms, which gives me, ∞ Ʃ...

Is it posible that the product of two different divergent series be a convergent serie?

Homework Statement Ʃ √n/(ln(n))^2 from n=2 to ∞ Homework Equations Series Test for convergent and divergent The Attempt at a Solution I tried doing ratio test and gotten [√(n+1)*(ln(n))^n] / [(ln(n+1))^(n+1) * √n] to find the limit, do...

Hello. I.m struggling to understand how to test for convergent and divergent. ∞ Ʃ (n/(n+1))^(n^2) n=1

Homework Statement evaluate or show that is divergent. Homework Equations \displaystyle\int_0^3 {\frac{1}{x-1}dx}The Attempt at a Solution \displaystyle\int_0^1 {\frac{1}{x-1}dx} +\displaystyle\int_1^3 {\frac{1}{x-1}dx}lim_{b->1^-} \displaystyle\int_0^b {\frac{1}{x-1}dx} + lim_{a->1^+}...

We know that a free scalar field on a diff-invariant 1+1 dimensional background (i.e. bosonic string theory on the worldsheet) contributes to the central charge of the Virasoro algebra with a constant term. Is there any examples of a 1+1d QFT that has instead a central charge contribution...

Just had a question from a coworker regarding how to tell if a series is convergent or divergent. Been a while since I've dealt with this so I thought I'd ask here. I *think* I remember that arithmatic series were convergent by nature, but a geometric series could be either convergent or...

Homework Statement ∫ a= 2 b = ∞ (dv)/(v^2+7v-8) Homework Equations I have attempted the problem and am confused as to why the integral is not divergent. The Attempt at a Solution I integrated the function by using partial fractions and came up with a result of...

Hi, Can Someone Elaborate the fluid(water) Characteristics Such as Velocity n pressure When it passes through a divergent Part. Actually The Fluid is pumped Out from A 0.5HP Centrifugal Pump and then made to pass through a Divergent Part.

Hi there, I am reading an article, but I faced the following problem, and I am wondering if it is well known fact. If the integral of a function on some interval is infinity, can we partition this interval into countable disjoint (in their interiors) subintervals such that the integral...

Homework Statement There exists a function f(x) such that the indefinite integral of 1/f(x) as x-> infinity diverges, and f(x) >= x for all values of x. Prove this function must be a linear polynomial. Homework Equations None that I know of.The Attempt at a Solution No idea where to start.

Homework Statement Determine whether the following series converges or diverges: \sum_{}^{} ( \frac{1}{3} )^{ln(n)} Homework Equations N/A The Attempt at a Solution See attached document.. I had my Calc 2 final today, and this was our hard problem...but I don't know if my method is valid...

Sometimes it is said that the probability distribution which does not add up to 1 still can be used to find relative probabilities. For example, consider probability distribution p_n = 1/n for all natural numbers. Does it make sense to say n = 1 is twice as probable as n=2, even if total...

can we simply truncate a Fourier series if it is divergent?? given a Fourier series of the form \sum_{n=0}^{\infty}\frac{cos(nx)}{\sqrt{n}} can i simply truncate this series up to some number finite N so i can get finite results ?? thanks.

Homework Statement Determine an explicit function for this sequence and determine whether it is convergent. an={1, 0, -1, 0, 1, 0, -1, 0, 1, ...} The Attempt at a Solution I came up with this function: an = cos(nπ/2), and wrote that as sigma notation from n=0 to infinity. Is...

Homework Statement For the sequnce an defined recursively, I have to determine the limiting value, provided that it exists. a1=2 and a(n+1) = 1/(an)^2 for all n Homework Equations The Attempt at a Solution Ok, so I 've done problems like this but the a(n+1) was biggger than...

$$ g'(\theta) = 2\sum_{n = 1}^{\infty}(-1)^{n + 1}\cos n\theta. $$ How can I show that this series diverges for all values other than $\pm\frac{\pi}{2}$?

Homework Statement Prove that the given sequence diverges to infinity. {an} = (-n^4+n^3+n)/(2n+7) Homework Equations Diverges definition The Attempt at a Solution So far I have: Let M>0 and let N= something. I'm having a hard time figuring out what N should equal for the...

My question is in regards to systems of ordinary differential equations. One of my research topics right now involves working with some complicated coupled ODEs used to model ecological stuff. Without getting into the details, the model I am working on now has a bad tendency to diverge for...

Homework Statement Ʃ (1+n+n2)/(√1+n2+n6)) n=1 to infinity Answer is divergentHomework Equations Comparison Test / P Series 0≤an≤bn The Attempt at a Solution Hello, I simplified the problem to Ʃ (1+n+n2)/(1+n2+n6)1/2 Is it incorrect of me to say immediately right here that because the power...

Series -- convergent or divergent? 1. Determine whether the following series is convergent or divergent. When a series is convergent, find the sum. If it diverges, find if it is infinity, - inf, or DNE. Ʃ [(1/na) - 1/ (n+1)a] 2. we are finding if a >0 3. I know that it...

Homework Statement I need to show that ##\displaystyle\int_\Omega (\nabla G)w dxdy=-\int_\Omega (\nabla w) G dxdy+\int_\Gamma \hat{n} w G ds## given ##\displaystyle \int_\Omega \nabla F dxdy=\oint_\Gamma \hat{n} F ds## where ##\Omega## and ##\Gamma## are the domain and boundary respectively...

Homework Statement ##\sum _{n=1}^{\infty }\dfrac {\left( -3\right) ^{n}} {n^{3}}## According to Wolfram Alpha the series diverges by the Limit Comparison Test, but I remember that the limit comparison only works with series greater than zero. How is this possible? Homework Equations...

I am to find whether the sum of (n!)/(n^n) converges or diverges. I tried both the limit comparison test, and a regular comparison test. (These are the only types of tests I am allowed to use.) So I tried several approaches: Approach #1: (n!)/(n^n) > 1/(n^n) Normally we use a setup like...

an = [cos (3n) )] /n.cos(1/n) My solution is , I wrote an as liman→∞ [cos (3n) )] /[ cos(1/n) / (1/n) ) . We get liman→∞ cos(3n) / ( 1/0 ) . I think solution of this limit is zero but ı'm not sure cos(3n) .I think cos(3n) as a number and number/infinity is zero .As a result of...