Sum Definition and 1000 Threads

Homework Statement Does this converge or diverge? Ʃ1/(1+2+3+4+5...+n), as n---> infinity?The Attempt at a Solution I rewrote this into Ʃ(Ʃ1/n) (is it correct?). I figured that since Ʃ(1/n) diverges, then the sum of each partial sum most (obviously) also diverge. However, it appears I'm...

Let $S=\{ 1, 2, \ldots , 2p\}$, where $p$ is an odd prime. Find the number of $p$-element subsets of $S$ the sum of whose elements is divisible by $p$.Attempt. Let $\mathcal{K}$ be the set of all the $p$ element subsets of $S$. Let $\sigma(K)$ denote the sum of the elements of a member $K$ of...

Homework Statement The division of a polynomial f(x) by (x – 1)(x – 2) has remainder x + 1. If the remainder of the division of f(x) by (x – 1) and (x – 2) are, respectively, a and b. Then what is a^2 + b^2? Homework Equations I guess the remainder theorem could be useful here. The...

1/5 + 1/7 + ..... + 1/401

Z is the set of integers. Prove that (3/7)Z + (11/2)Z = (1/14)Z Attempt: By definition, (3/7)Z+(11/2)Z={3k/7 + 11m/2 : k,m € Z} = {(6k + 77m)/14 : k,m € Z}. Showing that 3/7Z+11/2Z is a subset of 1/14 Z is easy but I can't prove the converse. Can't show that whatever n€1/14Z I take...

Homework Statement Find the derivative of y = x^2 + x^(2x)The Attempt at a Solution By looking at the equation I think I need to use implicit differentiation + natural logs. But I can't do anything with: lny = ln(x^2 + x^(2x)) So I assume I'm wrong.. Any help??

Homework Statement Here is the problem: Here is the solution: I am confused about part c. The Attempt at a Solution Here is my attempt at part c: I don't get why the answer key solution sums the moments about point G. I decided to sum up the moments about C and D and...

∞ Ʃ 1/(n(n+8)) n=1 So i used partial fractions and got (1/8)/(n) - (1/8)/(n+8) From there i pulled out the 1/8 so now my equation is ∞ (1/8) Ʃ (1/n)-(1/(n+8)) n=1 So from here do i just start doing like s1= (1/8)(1-1/9), s2=(1/8)(1/2-1/10) to find...

Hi, Is there a general algebraic expression for the sum of a function inside a radical? I mean for something like this? \sum^{n}_{i=1}\sqrt{f(i)} The specific case is given with constant c: \sum^{n}_{i=1}\sqrt{c^4i^4+c^2i^2+1} And I supposed a related question is that, is there some way of...

Hi, I'm writing a program in fortran that basically creates a loop from 1 until a certain number x (input by the user), and goes through each value between 1 and the certain number x in order to determine if each value meets certain criteria. The criteria is that the sum of the square of the...

I was working on some algebraic topology matters, thinkgs like the connected sum of some surfaces is some other surface. And for this study, I was using the Munkres's famous textbook 'Topology' the algebraic topology part. My qeustions are as follows: Q1) Munkres introduces 'labelling scheme'...

Hi everyone. I have learned that: 1+2+3+...=\frac{n(n+1)}{2} 12+22+32=\frac{n(n+1)(2n+1)}{6} I want to know what the general formula of Ʃna, in which n and a are natural numbers, respect to n and a.

From a fraction with infinite sum in denominator to partial fractions?? I am currently studying a course on Perturbation Methods and in particular an example considering the following integral \int_{0}^{\frac{\pi}{4}} \frac{d\theta}{\epsilon^2 + \sin^2 \theta}. There's a section of the...

S = \frac{1}{2} + \frac{1}{4} + ... + (\frac{1}{2^n}) I noticed that this is a sum of a infinite series with the common ratio being 1/2, so using \frac{1}{1-1/2} I get S = 2, however with this question there is a hint saying multiply S by 2, which I did not use so I'm worrying if I done...

The drawing show a barometer with water inside. If I move up object with air inside I recover PV energy (P=external pressure, V=volume of object). If I want to move out object when it is at top, I need PV, is that ? So if it's that. If I replace: 1/ gravity by balls attracted with springs (for...

Hi, I need your help, Say we have two random variables with some joint pdf f(x,y). How would I go about finding the pdf of their sum?

I need to calculate \sum_{n=0}^{∞}x^{(2^n)} for 0≤x<1. It doesn't resemble any basic taylor series, so I have no idea how to sum it up. Any hint, or the resulting formula? This series comes from a physical problem, so I suppose (if I didn't make a mistake) that the series is sumable, and...

Homework Statement If the weight of the boom is negligible compared with the applied 45-kN load, determine the cable tensions T1 and T2 and the force acting at the ball joint at A. Homework Equations The Attempt at a Solution I have successfully calculated the tensions in...

Provided is a function f(x)=\sum_{j=1}^n ||x-x_j||, for x being a two dimensional vector, where ||.|| denotes the Euclidean distance in 2D space. How could one obtain a derivative of such a function?

Having a lot of trouble with this question. So first I tried making an equation, and I wrote that the probability = P(rolling a 6)+P(rolling a 6 and not a 7 on the first roll and not a 9 on the first roll) + P(rolling a 6 and not a 7 on the first roll and not a 9 on the first roll and not a 7...

I know how to differentiate the dot and cross products of two vectors, is the differentiation of a vector sum done like this: d/dt (u+t) = u' + t + u + t' Or simply add them and then differentiate? Thanks

Homework Statement [SIZE="3"]\sum_{n=2}^{\infty} \frac{1}{n^2-1} Homework Equations The Attempt at a Solution After doing partial fraction decomposition, I discovered that it was a telescoping series of some sort; the partial sum being 1/2[ (1 -1/3) + (1/2 - 1/4) + (1/3 - 1/4)...

Homework Statement I need to prove both of these (in exercise 11) http://postimage.org/image/x7shxv11f/ Homework Equations The dot product The Attempt at a Solution

Homework Statement If the magnitude of the sum of two vectors is less than the magnitude of either vector, then: -the vectors must be parallel and in the same direction -the scalar product of the vectors must be negative -none of these -the scalar product of the vectors must be...

Homework Statement h(x)=\left\{\begin{matrix} 9+2x , 0<x<\pi\\ -9+2x , -pi<x<0 \end{matrix}\right. \\ Find \ the \ sum \ of \ the \ Fourier \ series \ for \ x=\frac{3\pi}{2} and\ x=\pi \\ The \ Fourier \ series \ is: \\ h(x)=9+\pi + \sum_{n=1}^{inf}...

http://books.google.rs/books?id=vrcHC9XoHbsC&pg=PA234&lpg=PA234&dq=Quantum+theory+of+magnetism+Ising&source=bl&ots=5uRLh1gzEf&sig=ZNHUXGgzbDIW4nHy3Txdmi4mGb8&hl=sr&sa=X&ei=YORpUN6ZO7HN4QTwnoDgAw&ved=0CEsQ6AEwBA#v=onepage&q=Quantum%20theory%20of%20magnetism%20Ising&f=false In page 266 why we...

Ok so I already know how to solve it by looking at an example my teacher did in class... This is what I did... 4. A 2.00 kg block is held in equilibrium on an incline of angle θ = 70° by a horizontal force vector F applied in the direction shown in the figure below. If the coefficient of static...

I have seen double sums, but have come across a problem involving sums over primes. However, this sum is inside a second sum, and is taken over all primes that divide the outside index, like this: \sum_{k=1}^{n} \sum_{p | k} \frac 1p for p prime. Is there any way to manipulate this...

Homework Statement 14 Ʃ 2(4/3)^n n=1 Homework Equations Sn=a(1-r^n)/(1-r) The Attempt at a Solution 2(1-[4^14]/[3^14])/(-1/3)=330.74 However, the answer sheet gives ~441 as the answer, and I confirmed it by doing it by hand. Why is the equation not working? What's wrong?

Serie's sum of 2/n*7^n? How do we find it's sum for n=1 to n=inf? I really do not know how to start, wolfram alpha gave me the answer, but I'm not making any sense out of it. http://www.wolframalpha.com/input/?i=n%3D1+to+n%3Dinf+2%2F%28n*7%5En%29+sum

Homework Statement Find the exact sum of: \sum 2/(n7n) n=1->∞ The Attempt at a Solution Let Sn denote the nth partial sum. ln(Sn) = \Sigma ln(2/(n7n)) =\Sigma ln2 - lnn - nln7 = nln2 - (ln1 + ln7 + ln2 + 2ln7 + ln3 + 3ln7 ...) = nln2 - ln(n!) - ln7\Sigma n = ln (2n)/n...

This is born out of musings around coalition governments that arise from the party with the most votes not achieving ≥50% of the votes (as opposed to emergency coalitions). Taking the figures below how would one go about determining all the possible combinations of parties who combined have...

Homework Statement Find the sum value of capacitors. Homework Equations The Attempt at a Solution I tried to redraw the scheme like in the picture below, but my teacher told me it's not correctly redrawn. I hope You'll prove to me that my redrawn scheme is correct... If not I'm more than...

Homework Statement For any positive integer n determine: \sum\limits^n_{i=0} \frac{1}{i!(n-i)!}Homework Equations I don't really know where to start.. Up until this point we've just been doing permutations, combinations, and determining the coefficient of a certain term in the expansion of a...

I observed the following: 1) $\sqrt{2}$ is irrational. 2) $\sqrt{2}+\sqrt{3}$ is irrational(since its square is irrational). 3) $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational(assume its rational and is equal to $r$. Write $r- \sqrt{5}=\sqrt{2} + \sqrt{3}$. Now square both the sides and its...

Homework Statement I need to show that the lim n->inf ( [(1/n) * sum from k=1 to n of ln(k) ] - ln(n) ) is equal to the lim n->inf ( (1/n) sum from k=1 to n of ln(k/n) ) The Attempt at a Solution I showed that the sum of ln(n) from k=1 to n is ln(n!) using ln(a) + ln(b) = ln(a+b). I...

Homework Statement Referring to the vectors in the figure, express the sum A + B + C in unit vector notation. http://i.imgur.com/ajMkK.pngHomework Equations I'm not sure if it wants me to add Dy, I've tried it both times and masteringphysics won't take either answer.The Attempt at a Solution...

I have thought about it and every-time I think I have an answer I try to explain it to myself and I fail. I want an intuition behind it and if there is a proof better. Thank you

Prove the formula $$ \sum_{k=1}^{n}e^{ik\theta} = \frac{e^{i\left(n+\frac{1}{2}\right)\theta}-e^{i\frac{\theta}{2}}}{2i\sin\frac{\theta}{2}} $$ I have a hint that says consider the expression $e^{i\left(n+\frac{1}{2}\right)\theta}-e^{i\left(n-\frac{1}{2}\right)\theta}$. How can I get the second...

I was looking at finding a series solution to a 2nd order DE the other day and came up with the following (for one of the solutions, and there was a somewhat similar series for the other solution). \sum_{k=0}^{\infty} \frac{x^{3k}}{(3k)!} \prod_{m=1}^{k-1} (3m+1) Wolfram said the solutions...

State the special cases of the above two formulas for $n = 0, 1,$ and $2$. These should be familiar formulas. I don't see what is so special and familiar about when n = 2 or for cosine n = 1.When $n = 0$, we have $$ \sum\limits_{k = 0}^0\cos k\theta =...

I have a homework question which asks about Reimann sums (which I feel relatively comfortable with), but I just don't know what they're asking. Here's the image https://dl.dropbox.com/u/38457740/maff.bmp

Homework Statement Within the xy-plane, two vectors having lengths P and Q rotate around the z-axis with angular velocities ω and –ω. At t = 0,these vectors have orientations with respect to the x-axis specified by θ1 and θ2. How do I find the orientation of the major axis of the resulting...

If I graph $x+ \sin x $ it looks like a wavey line. I want a function that looks like a wavey circle. I thought $\sqrt{r^2-x^2}+\sin x$ may work and played around with values for r, no such luck. Does anyone know a function to achieve this?

Consider the infinite sum: \sum_{n=1}^\infty \frac{n^2}{2^n} For the impatient of you, the answer is here. Anyways, I'm trying to generalize this result, so let me state a definition: \sigma_\alpha(k) = \sum_{n=1}^\infty n^k \alpha ^ n This sum converges so long as the magnitude...

this is a riemann sum question and i need help with part 2 let Sn denote the finite sum 1+2^ 3/2 +...+n^ 3/2 i) use suitable upper and lower riemann sums for the function f(x)=x^3/2 on the interval [0,100] to prove that S99<J<100 ummm i did this and found 40000<J<41000 II) hence, or...

*SOLVED*Riemann Sum Question *SOLVED* My question is quite simple. I probably just missed something somewhere. I've looked for hours and cannot find the mistake. Homework Statement Find the area under the curve using the definition of an integral and Gauss summation equations: f(x) = 3 -...

Hello, I am now studying centripetal force. and the problem is that centripetal force in gravitational field. Let's talk about Ferris-wheel ride, this ride has some rooms to carry people and fixed to the edge of the wheel. Since it is rotating periodically, its magnitude of net force...

I know I should know this, but how would one convert a typical integral into a Rieman Sum? ∫0n sinx + x dx for whatever n. for example.

Homework Statement let f(x)=x^2 Calculate upper sum and lower sum on the interval [-2,2] when n=2The Attempt at a Solution since n=2 I divide the interval into [-2,0]\cup[0,2] then on the interval [-2,0] the function f(x)=x^2 has the highest valute at x=-2, f(-2)=4=M_{0} and the lowest value...