Divergent Definition and 193 Threads

Is it possible to re-arrange the terms of a divergent series such that the re-arranged series converges?

Hi everybody! I'm a new Physics Forums user and hope someone could help me out with my minor dilemma. I'm a PhD student in mathematical/theoretical physics and I' working on the Boltzmann equation in QFT. Up to now, there was no major emphasis on Feynamn diagrams - the approach was rather more...

1. A year after the leak began the chemical had spread 1500 meters from its source. After two years, the chemical had spread 900 meters more, and by the end of the third year, it had reached an additional 540 meters. a. If this pattern continues, how far will the spill have...

convergent or divergent?? Homework Statement i took a calc 2 quiz today and had a question on one of the. it's too late to correct what i did, but it's never too late to learn it for the final haha here is the problem they want us to find the sum of the series (below) from 1 to...

Homework Statement Determine whether the series converges or diverges. \sum 3+7n / 6n Attempt : Comparison test : 3+7n / 6n < 7n / 6n 3+7n / 6n < (6/7)n since (6/7)n is a geometric series and is convergent is 3+7n / 6n convergent as well?

Homework Statement Determine whether the series is convergent or divergent. \sum n5 / (n6 + 1)

Homework Statement Determine whether the series is convergent or divergent. 1 + 1/8 + 1/27 + 1/64 + 1/125 ... Homework Equations The Attempt at a Solution I know this is convergent but not sure how to prove this mathematically.

Homework Statement Show that if: lim_{k\to\infty}b_k\to+\infty, \sum_{k=1}^\infty a_k converges and, \sum_{k=1}^\infty a_k b_k converges, then lim_{m\to\infty} b_m \sum_{k=m}^\infty a_k = 0 Homework Equations The Attempt at a Solution I only have an idea why this is true--\sum a_k...

I'm trying to understand a paper in which the authors use a number of test functions (are they the same as convergence factors) to make integrate unintegrable functions. Now here is my ignorant question: why is this acceptable? The product of the original function and the test function or...

I got a series in the following form \sum_{k=0}^\infty\dfrac{k!}{c^{2(k-1)}} where c is arbritary complex constant, how can I show this series is divergent? Thanks

if we can proof an statement but we make use of a divergent series or integral to proof it.. would it be considered valid ?? for example using the theory of distributions or divergent series you can always prove the Riemann Functional equation.

Homework Statement Suppose that (x_n) is a properly divergent sequence, and suppose that (x_n) is unbounded above. Suppose that there exists a sequence (y_n) such that limit (x_n * y_n) exists. Prove that (y_n) ===> 0. Homework Equations (x_n) ===> 0 <====> (1/x_n) ===> 0...

If a power series, \sumc(subk)*x^{k} diverges at x=-2, then it diverges at x=-3. True or False? I said true, but was confused by my reasoning. Does anyone have any suggestions?

1)summation for n=0 to infinity for (n!/n^n)*exp^n. Can anyone help to prove whether this is convergent or divergent?

Homework Statement Determine whether or not the series \sum^{\infty}_{n=1} \frac{1}{\sqrt{n+1}+\sqrt{n}} converges. The Attempt at a Solution Assuming this diverges, I rationalize it to get get \sum^{\infty}_{n=1} \sqrt{n+1} - \sqrt{n}. How would I proceed further? Is this even the...

http://en.wikipedia.org/wiki/George_F._Carrier" :confused:

Hi, I am trying to calculate a double integral, in Mathematica it could be denoted Integrate[(x*y)/(x*y-m2/s2),{x,0,1},{y,0,1-x}] That is, \int\int\frac{xy}{(xy-m^{2}/s^{2})}dydx with boundaries y=0,y=1-x and x=0,x=1. m and s are constants, of course. Now, I get some fairly...

if we can obtain resummation methods for divergent series such as 1-1+1-1+1-1+1-1+... or 1!-2!+3!-4!+.. my question is why is there no method to deal with divergent integrals like \int_{0}^{\infty} dx x^{s-1} or \int_{0}^{\infty} dx (x+1)^{-1} (x^{3}+x)

I don't even know where to start this one. I can do all the other problems in the section, but this one makes no sense

I'm looking for help with my conceptual understanding of part of the following: 1) If a series is convergent it's nth term approaches 0 as n approaches infinity This makes perfect sense to me. 2) If the nth term of a series does not approach 0 as n approaches infinity, the series is...

Homework Statement (a) Show that \sum \frac 1n is not convergent by showing that the partial sums are not a Cauchy sequence (b) Show that \sum \frac 1{n^2} is convergent by showing that the partial sums form a Cauchy sequenceHomework Equations Given epsilon>0, a sequence is Cauchy if there...

For lim n->infinity n^-(1+1/n), the p series test shows that it converges since (1+1/n) will be greater than 1, while doing a limit comparison test with 1/n gives 1 showing that it diverges since 1/n diverges. For which one is my thinking wrong about?

from n=1 to infinity does the series converge or diverge? n!/n^n its in the secition of the book with the comparison test and limit comparison test. if you compare it with 1/n^n (this is a geomoetric series) you get a= 1/n amd r= 1/n but in the thrm r = to some finite number...

If I have (a_n + b_n)^n = c_n where a_n is convergent and b_n divergent. Is c_n then divergent? And what if a_n and b_n were divergent, would c_n be divergent also? but what if they were both convergent then surely c_n is convergent right? I can't see a rule or a theorem that tells me...

Homework Statement Problem is to determine if this is convergent or divergent: n = 1 E infinity (27 + pi) / sqrt(n) Homework Equations p-series test? The Attempt at a Solution I was looking at this problem, It looks as if the p-series may apply, it is continuous, decreasing...

If the problem of renormalization is that there are divergent integrals for x-->oo couldn't we make the change. \int_{0}^{\infty}dx f(x) \approx \sum_{n=0}^{\infty}f(nj) using rectangles with base 'j' small , and approximating the divergent integral by a divergent series and 'summing' by...

Are there any method to deal with divergent integrals in the form \int_{0}^{\infty}dx \frac{x^{3}}{x+1} \int_{0}^{\infty}dx \frac{x}{(x+1)^{1/2}} ? in the same sense there are methods to give finite results to divergent series as 1+2+3+4+5+6+7+... or 1-4+9-16+25 or similar

Homework Statement Find the limit of sequence if it converges; otherwise indicate divergence. a_n=(5-9n+6n^4)/(7n^4+5n^3-3) answers a=6/7 b=-2 c=5/7 d=diverges Homework Equations none The Attempt at a Solution The limit of A_n is equal to 6/7 which is one of the...

I was wondering if anyone could tell me more about the Riemann Zeta function, esp at negative values. Especially when \sum_{n=1}^{\infty}n= \frac{-1}{12} R where R is the Ramanujan Summation Operator. Could anyone post a proof?

is the series covergent or divergent? I want to know that is the following series convergent or divergent?? \sum \frac{2}{\sqrt{n}+1} when i apply divergent test to it, it comes equal to 0 , it means that divergent test gets failed. then how to solve it? which test i should apply...

I want to know if the integral \int_0^{\infty} dx/(4x^3 + x^(1/3)) is convergent or divergent?Thanks

let be the divergent series: 1^p+2^p+3^p+.....+N^p=S(N) with p>0 my question is..how i would prove that this series S would diverge in the form: S(N)=N^{p+1}/p+1 N--->oo for the cases P=1,2,3,... i can use their exact sum to prove it but for the general case i can not find any...

let be the completely divergent series at \epsilon\rightarrow{0} in the form of: \sum_{n=0}^{\infty}\frac{a(n)g^{n}}{\epsilon^{n}} where g is the coupling constant of our theory..then let,s suppose this series is summable and that we can get the correct result S S=S(g,\epsilon) then...

I just have a quick question, is cos and sin divergent or convergent? I keep getting mixed results from different sources. I know that both functions oscillate so on the interval [0, infinity) they both diverge. But for some of my homework problems relating to improper integrals, the book...

Hello, I'm working on this problem: Prove that for any real x, the series SUM n=2 to infinity of 1/(log n)^x diverges. So far, I have applied the test that says that if SUM 2^n*a_2n converges then the series converges. I got: 1/log2*SUM 2^n/n^x I know that 1/n^x converges if x>1, but...

if we know that the divergent series in perturbation theory of quantum field theory goes in the form: \sum_{n=0}^{\infty}a(n)g^{n}\epsilon^{-n} with \epsilon\rightarrow{0} then ..how would we apply the renormalization procedure to eliminate the divergences and obtain finite...

Hello, according to theory of alternating series, the series \sum_{n=0}^\infty (-1)^n is not convergent, correct?. Howcome maple estimates it as \sum_{n=0}^\infty (-1)^n = 0.5000000000. This seems strange to me.. Why this strange result?

Hi, I need to show that the infinite series 1+ 1/3 + 1/5 + 1/7 + 1/9 + ... diverges. Am I correct in saying that it is a subsequence of the divergent harmonic series, therefore diverges? Is there some other more elaborate (and correct) way of grouping the terms to show that they are greater...

\int_9^{inf} \frac{1}{x^{6/5}} first thing i did was found the integral of the function \frac{5}{x^{-1/5}} then plug in inf(i will name it b) and 9 \frac{5}{b^{-1/5}} - \frac{5}{9^{-1/5}} now i will find the lim -> inf well for \frac{5}{9^{-1/5}}, it's equal to 7.759 now for...

I need help with two questions. Find a divergent improper integral whose value is neither infinity nor -infinity. 2. Find the volume of an ellipsoid (a^2*x^2) + (b^2*8y^2) + (c^2*z^2) = a^2*b^2*c^2 using integration.

If you want to calculate the electric field at a distance r from a line of infinite length and uniform charge density you could one of three things: 1. Employ symmetry and Gauss' law. 2. Use superposition and integrate from minus to plus infinity along the rod. 3. Integrate to find the...

Determine change in velocity across ideal divergent nozzle with inlet enthalpy of 1,204 Btu/lbm and exit enthalpy of 1,203.91 Btu/lbm I know that delta v^2=(.09btu/lb)*(2)*(32.2lbm*ft/lbf sec^2)(778ftlbf/btu) so: deltav^2=4509.29ft^2/sec^2 taking the sqrt deltav=67.15ft/sec My...

How is this made?..in fact from having infinites you sum them and have a finite number...i do not know how you can do it..what techniques of maths are used.and if this would be valid for making any series convergent or have a finite number...i think you use divergent series math theories..could...