Comparison Definition and 393 Threads

Homework Statement Find if the sum from n = 1 to infinity of (n^n)/n! diverges or not. Homework Equations p = an+1/an The Attempt at a Solution Using the comparison test I get to the point where p_n = (n+1)^(n+1) / [(n+1) n^n] Shouldnt p just be 0, don't (n+1)^(n+1) and n^n...

Homework Statement I need to show that: \sum_{n=1}^\infty \frac{n^{2}}{2^n} converges. I know I can compare it with the larger convergent geometric series: \sum_{n=1}^\infty \frac{1.5^{n}}{2^n} Which is larger for all terms for n> 13. My question is, I found this "13" through trial and...

Homework Statement \sum^{\infty}_{n=1} \frac{e^{n}+n}{e^{2n}-n^{2}} Homework Equations I have to use either the Comparison Test or the Limit Comparison Test to show whether the series converges or diverges. The Attempt at a Solution a_{n} = \frac{e^{n}+n}{e^{2n}-n^{2}} b_{n} =...

Homework Statement Using the comparison test determine if the infinite series for sin(3/n^2) converges or diverges. The Attempt at a Solution Well... these are pretty straight forward, and it's pretty obvious that this is convergent, but I'm having trouble applying the...

I read a proof for showing that the harmonic series is a diverging one. This particular one used a comparison test: 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ... + 1/16 + ... 1/2 + 1/2 + 1/4 + 1/4 + 1/8 + 1/8 + 1/8 + 1/8 + 1/16 +... + 1/16 + ... Each term in the second series is <...

Hello everyone! I am taking my Physics Ph. D. Qualifier on Friday and Saturday. During Saturday's exam we will be tested on E&M and Thermodynamics/Statistical Mechanics. We get to take 2 books to each exam, so I basically can take 1 Thermo Book with me (I'm also taking Griffiths on Saturday)...

sum(1/n!,n,1,inf) the only thing i can think of is 1/n^2>=1/n! , 1/n^2 being a convergent p series since p >1 thus /n! is convergent

14. sum(n^(1/2)/(n^2+1),n,1,inf) b=n^(1/2)/(n^2+2)<=n^(1/2)/(n^2+1)=a b is conv since lim as n-> inf b = 0 since n^(1/2)<n^2+2 for x>=1 thus a is conv i have a feeling this is a shakey way to do this if its even correct somone pleae clarify the solution to this problem

Homework Statement I have two relatively similar problems: 1.) Sigma n=1 to infinity ((ln n)^3 / n^2) 2.) Sigma n=1 to infinity (1 / sqrt(n) * (ln n)^4) I'm to prove their convergence or divergence using either the direct comparison test or the limit comparison test. I understand...

It's a great joy to capture small creatures big on the screen without them even noticing it. There are several ways to do that. I used to utilize my old Panasonic FZ-18 bridge camera with a close up lens. Preferably #2 or 2 dioptries or 50 cm focus distance, with a moderate zoom 8-12x you get...

Homework Statement I was just wondering that when applying a comparison test or a limit comparison test, do i have to show that a comparison test does not work in order to use a LCT? Also, if i directly use LCT, will i get the same answer as in the regular comparison test? Thanks...

Homework Statement Computational Fluid Dynamics anyone? :D I know someone out there is a genius? I'm trying to understand some of the differences between Experimental results and a Fluent (CFD) analysis of a NACA 0012 aerofoil. There are 3 Cp/x graphs of my results (plotted with negative down...

Homework Statement Look at the diagram accompanying the question. Which has least C-H bond energy? The Attempt at a Solution On cleavage of a C-H bond, a carbanion is formed as carbon is more electronegative than hydrogen. So cleavage of (b) results in a carbanion stabilized by resonance

http://img205.imageshack.us/img205/5117/summation.jpg I think next step is: http://img205.imageshack.us/img205/7044/summation2.jpg but the questions are: how & why? why is that the next step? how do I solve such problems?\how do I choose the second part?

Hi All I'm looking for a table of Tcs and normal state resistivities for a selection of 'typical' superconductors. I'm sure such a thing must exist in literature, but I'm having trouble locating it. Specifically, I've just finished a dissertation project developing a measurement technique...

hi Is there any document about the difference between U235 and U238 properties?

Homework Statement Two resistors of resistances R1 and R2, with R2 > R1, are connected to a voltage source with voltage V0. When the resistors are connected in series, the current is Is. When the resistors are connected in parallel,the current Ip from the source is equal to 10 Is. Let r be...

Homework Statement Compare the deBroglie wavelength for an electron in the n=6 orbit of He+ compared to the n=2 orbit. Is the deBroglie wavelength the same, smaller, or larger? Derive this. Homework Equations Quantization of Paths of Electrons: 2 pi r = n (lambda) Bohr Radius: rn=n2 aB The...

I want to purchase a dental magneostrictive ultrasonic scaler. I need help with comparisons on technical specifications. Can anyone help me determine what is the best unit as far as output goes, if I give you the specifications? (Obviously I do not know electrical stuff - Just teeth)

Homework Statement (a) Let f,g: [a,b] \rightarrow \Re. Define: f \vee g(x) = max(f(x),g(x)), x\in [a,b] f \wedge g(x) = min(f(x),g(x)), x\in [a,b] (b) Let f_{+} = f\vee0, f_{-} = -(f\wedge0) Show that: f = f_{+} - f_{-} abs value of f = f_{+} + f_{-}...

hey guys I'm kind of stuck on this idea of the comparison test. i understand the process and how it is done but i don't seem to understand how to find the second series(typically called bn) to compare with the original. get what i mean? thanks! =)

I have been reading a paper which introduced classical mechanics concerning only one dimension. Before we get into anything about displacement and velocity, I read about dimensional analysis. There is a section of the paper which isn't very well explained and I hope someone can explain it to...

Homework Statement Which two of the three types of fields in the title of this are thread are the most similar? Provide supporting evidence? Homework Equations Gravitational: -Source: point mass -Field intensity proportional to: M/r^2 -Range: long range -Strength: weak -Direction of field...

How do GM crops (both current and potential in the near future) compare with organic in terms of output per acre? How does it compete with such methods as Fukuoka Natural Farming, and other forms of permaculture?

Homework Statement I am comparing a normal DNA decamer molecule with one in which the two strands are only connected by the two base pairs on one of the ends. It was determined that the potential energies of both DNA molecules are negative, with values for the normal DNA much more negative...

Hello, folks. This happens to be my first post here, and I've come with a question from a problem set in my textbook. Homework Statement Determine whether the following series converges or diverges. Give reasons for your answer. Homework Equations \sum^{\infty}_{n=2}...

I am trying to compare the fluid velocity given by the closed form solution and FEA analysis for fluid flowing through a channel that is 800u long and 100u wide. I am using the equation vmax= (gradP)*(radius)^2/(4*viscosity) I got 8.4cm/s in the former compared to ~10cm/s in the latter...

Disclaimer: Although my question is targeted toward the UK, I do not wish to exclude comparison with other countries e.g. Germany or Canada. Please, if you have studied maths at universities in another country, your experience is of value and interest. Here in the United States, the usual...

Homework Statement For what values of p does the following integral converge or diverge? \int^{\infty}_{2}\frac{dx}{x[ln(x)]^{p}} The Attempt at a Solution I have graphed y=\frac{1}{x[ln(x)]^{p}} for different values of p (negative, zero, positive), and it looks as though in all...

If we think of two isolated systems, A and B, existing side by side, the proportion of the energy between those systems should always stay the same. Here is a thought, that I would like some comments on: System A contains a planet, and the advanced civilisation on this planet, have created...

Does anyone have any knowledge on these? I look at an example of a direct or limit comparison and i see what they are doing, but I have no idea how they got the "comprable" term... for example the sum (n = 1) to infinity n/(n^2 +1) you can use either test, but how do you choose what to...

I need to compare two ICE engines. I need to know the "work" of one compared to another. Let's say the first engine has a bore of 3'' and a sroke of 3" connecting rod 5.25. If you need cylinder presure,say PCP is 5000psi At 20 degrees ATDC and tapers to 800psi at 90 degrees ATDC. The second...

typedef struct Emp { unsigned char lname[MaxName + 1]; /* + 1 for '\0' */ unsigned char fname[MaxName + 1]; unsigned int id; unsigned char dept; bool married; } Emp; int comp1(const void* item1, const void* item2) { const Emp* emp1 = (const Emp*) item1; //emp1...

Hi everyone, I need your help badly. This may sound simple to everyone but I need to get the concept sorted out. For ratios, we know that it is a comparison between 2 or more quantities with the same units. My question is, can ratio be used to compare between say ingredients in a...

I am confused about the right formula for this. Is it R_{n} \leq T_{n} \leq \int_{n+1}^{\infty} or R_{n} \leq T_{n} \leq\int_{n}^{\infty} ? Say for example, I want to estimate the error in using the sum of the first 10 terms to approximate the sum of the series. The textbook seems to use...

I have been given the series sum 1/sqrt(3n-2) from n=1 to infinity I am supposed to use the limit comparison test, and the comparison series my book suggests is sum 1/sqrt n from n=1 to infinity, which I know is a divergent p series However, when I take the limit of one divided by the...

Hello everybody! I have a large set of items and, two-by-two, there exists some kind of attraction/repulsion that I have measured. I synthesize this information in a (nxn) matrix. Under different circumstances this attraction/repulsion changes. So, what kind of statistical/mathematical...

Hello everybody! I have a large set of items and, two-by-two, there exists some kind of attraction/repulsion that I have measured. Under different circumstances this attraction/repulsion changes. So, what kind of statistical/mathematical procedure can I use to measure whether the changes...

Not really a specific question, but I am really struggling with the comparison tests for infinite series. I just finished doing quite a few problems from the section. I went in pretty confident, but after completing the section I was bummed that I only did a less than a handful correctly. My...

I'm not sure where to post this one but i'll start with the mechanical guys first. There are two different motors that share identical ratings but different sizes physically. They are represented as though they perform the same work, share a common HP and KW rating and the mechanical device...

Is the same inductance formula valid for a coil made of hollow tubbing that for a solid wire made , with both having the same width?, and supposing that a high frequency current flows through it whats the skin effect influence on the result

Homework Statement is the series convergent or divergent. Sum from 2 to ∞ of 1/ [n(ln n)^.5] Homework Equations comparison test? The Attempt at a Solution Is it possible to use the comparison test for this problem. Also, could I compare this with something like: (1/[(ln n)^.5]...

Homework Statement Use the Comparison Theorem to determine whether the integral below is convergent or divergent: e^-x / sqrt x dx integrated from 0-->1 The Attempt at a Solution I think it is convergent because 1/e^x is convergent. I set the original integral less than or equal to the...

Homework Statement \sum\limits_{n = 2}^\infty {\frac{{\sqrt n }}{{n - 1}}} Homework Equations The Attempt at a Solution \begin{array}{l} a_n = \frac{{\sqrt n }}{{n - 1}},\,\,b_n = \frac{{\sqrt n }}{n} = \frac{{n^{1/2} }}{n} = \frac{1}{{n^{1/2} }}\,\,{\rm{is_ a_ p - series_...

[SOLVED] Comparison of sound waves in air and underwater Homework Statement In air, the human ear is most sensitive to sound waves of 3300Hz. The auditory canal is part of the human ear. It is a tube of length 0.025m, i.e. 1/4 the wavelength of sound with frequency 3300Hz. When under...

Just want to get some terminology right. Is TOE equivalent to QG? If so is QG more frequently used by physicsts as it sounds more professional or simply more logical?

Homework Statement Does xn converge (Sum from n=1 to infinity) of xn = 1/(n + SQRTn) Homework Equations Using comparision test The Attempt at a Solution I separted into fractions of 1/SQRTn - 1/(1 + SQRTn) and i know that both of these diverge since the power of n is less than...

Hi all, I have been looking for an answer to this and I cannot find one. So here is my question... The surface area of 57mm twin round throttle body set-up was 5100 mm^2 and the single 75mm throttle body set-up was 4415 mm^2. Now to the actual question... Does smaller (twin)...

Use the Comparisom Theorem to determine if f(x) = \int^{\infty}_{42} \frac{42+42^-x}{x}dx is convergent or divergent. I compared it to g(x)=\int^{\infty}_{42} \frac{1}{x}dx \int^{\infty}_{42} \frac{1}{x}dx = Lim_{t->\infty}\int^{t}_{42} \frac{1}{x}dx Take the antiderivative, and the limit...

Homework Statement The diagram shows two wires; wire 1 and wire 2. The charge carriers in wire 1 (of circular cross section and radius R) have a drift speed down the wire that is not constant across the wire. Instead, the drift speed rises linearly from zero at the circumference (r=R) to at...