Homework Statement
A line of buckets numbered 0,1,2... extends indefinitely to the left with an elephant behind each bucket. Initially, all of the buckets are empty but then peanuts start falling into bucket 0 at a rate of one per second for 2^12 seconds. Whenever 5 peanuts accumulate in a...
hi guys, new user, long time lurker.
the following simple proof is proposed with the highlighted summations. you do not need to know what the proof is of to answer my question (it is that the payoff for a skew symmetric game, rock paper scissors, is zero). i need help understanding how you...
My understanding of the Einstein Summation convention is that you sum over the repeated indices. But when I look at the metric tensor for a flat space I know that
g^{λ}_{λ} = 1
But the summation convention makes me think that it should equal the trace of the matrix g_{μσ}. So it should...
Homework Statement
Hi
I was trying to understand an algorithm analysis problem and I came to this point:
[PLAIN]http://img820.imageshack.us/img820/1834/unledytw.png
can someone explain me what he did there? Is there any other step between that should have been written in order for...
How can I show that \sum_{i=1}^n\;\frac1{i(i+1)}=\frac{n}{n+1}
I've already figured out i can write it as \sum_{i=1}^n\;\frac1{i}-\sum_{i=1}^n\;\frac1{i+1}
but as I'm a little drunk I can't figure out how to get from there to the formula.
Sorry if I put this in the wrong sextion, but...
I'm trying to figure out what the summation notation of
(1-x1)^θ * (1-x2)^θ * ...(1-xn)^θ would be for summation
I know I need to convert this to a summation notation in order to solve my problem, but I can't figure out how to convert it. Any help will be appreciated.
Why is the Gauss summation formula for complex parameters a,b,c: \displaystyle _2 F_1 (a,b;c;1) = \frac{\Gamma (c) \Gamma (c-a-b)}{\Gamma (c-a) \Gamma (c-b)} only valid for \text{Re}(c-a-b)>0,\;c\neq 0,-1,-2,-3,...?
Homework Statement
Write a C++ program to determine and print the sum of the series (1/3 + 1/6 + 1/9 + ... + 1/(3*n)) for a given value of n. In case you don't see the patter, the series can also be written as 1/(3*1) + 1/(3*2) +1/(3*3)+ ... + 1/(3*n). The value of n should be given...
Homework Statement
Show that the summation notation satisfies the following property:
\displaystyle\sum\limits_{i=1}^n(\displaystyle\sum\limits_{j=1}^m aij) = \displaystyle\sum\limits_{j=1}^m(\displaystyle\sum\limits_{i=1}^n aij)
Homework Equations
N/A
The Attempt at a Solution...
I'm doing my masters thesis on ewald summation, I am searching for proper study materials for that... what I have is only papers(which you know doesnot explain everything they do!). It would be of great help if you can find me a few sources.. Please help. Thanks.
Homework Statement
Evaluate the sums: \sum^{n}_{i=1}ia^{i}
Homework Equations
The Attempt at a Solution
I'm assuming that because there's no limit or anything, the professor wants an equation. I know \sum^{n}_{i=1}i is \frac{1}{2}n(n+1) and \sum^{n}_{i=1}a^{i} is \frac{a^{n+1} - 1}{a-1}-1...
Hi everyone,
Could someone please tell me how to get MATLAB to do the following seemingly simple task..
j=1:3;
k1=1:3;
m=eye(3)
plot(j,symsum((p8+k1(j)).*m(p8,j),p8,1,3))
or,
k=1:3;
plot(j,sum((k+k1(j)).*m(k,j)))
Thanks for any suggestions,
Kate
Homework Statement
Homework Equations
The Attempt at a Solution
Obviously I don't need a solution because it's right there. What I need to understand is what happened after the third equation sign and more importantly, how would I learn to solve these kinds of problems on my own. I looked at...
Homework Statement
I'm not very proficient with LAtex, so I'll try to translate this mess the best I can. It's a summation
\sum i2 (on the bottom, there would be an "i = 1") (on the top, there would be an "n") this summation equals \frac{n(n+1)(2n+1)}{6}
In the summation, basically, "i"...
Homework Statement
\omega^2=(2/M)\sum_{n>0}\frac{A\sin(nk_0a)}{na}(1-\cos(nKa))
A, a, and k_0 are constants, n is an integer.
I need to find \omega^2 and \frac{\partial\omega^2}{\partial K}, but I have no idea where to start.Homework Equations
Not sure, the stuff above.The Attempt at a...
Dear all,
I have a problem with regard to the summation which is done inside the Do-Loop iteration. I have attached the file which includes further information about the defintions, some examples and etc.
Please help me to get the right codes in order to express totalu1, totalv1, totalu2 and...
Hi,
I have been staring at this for a while. I under stand the process and can account for and reproduce every step of this problem EXCEPT I can nit figure out where the 6i/n coms from. I have included the equation and the issue is highlighted in yellow.
Please explain... this is the last...
Hi,
What is the maximum value of the given summation in terms of k, l and N ?
max_{0\leq x \leq k} \sum_{(l_1,l_2)\in A} \frac{N!}{(N-l_1-l_2)!l_1!l_2!} x^{l_1}(k-x)^{l_2}(1-k)^{N-l_1-l_2}
where A=\{(l_1,l_2)|l_1,l_2 \in \{0,1,2,...,N\} and l_1+2l_2=l\} and 0<k<1.
Thanks a lot for your...
Homework Statement
Find the Summation Notation and Radius of Convergence of this series.
5, x, 10, x, ...
The Attempt at a Solution
I don't know how did they come up with that equation.. But the summation seems right.. Can anyone tell me how did they arrive with that equation? I've tried...
Find the sum of n terms of the series:
7/(1.2.3) - 17/(2.3.4) + 31/(3.4.5) - 49/(4.5.6) + 71/(5.6.7) - ...I know how problems like the following are solved :
1. 1/(1.2.3) + 2/(2.3.4) + 3/(3.4.5) + ...
2. 3/(1.2.4) + 4/(2.3.5) + 5/(3.4.6) + ...What will be the general term of the required...
Hi,
Can every body solve this problem in terms of a and b .
e^{-(a+b)}\sum _{n=0}^{\infty} \frac{a^n}{n!} \sum_{m=0}^{n}\frac{b^m}{m!}
Thanks in advance for your participation.
Homework Statement
show whether or not x(t) = cos(t) + sin(\sqrt{2}*t)
is periodic
The Attempt at a Solution
the first period
is
T1 = 2\pi
the second period is
T2 = \frac{2\pi}{\sqrt{2}}
how can I determine whether it is periodic or not?
in my book(about signals...
Along with some friends, i was trying to calculate the end product of a series(x^(1-x)). I for a finite value, i got a number close to arcsinh(SQRT 6), and by comparing the functions i believe it converges at infinity. However, i am unable to 100% prove this, and i am asking if the summation is...
Dear all,
Iam trying to get the right codes so that the summation could be done in the Do-Loop function using Mathematica.
The problem is that I could not get the summation for sumU1 and sumV1 to start from 1 using my codes as attached (Summation2.nb).
Please help me to improve the...
Hi,
First term is 10 and common ration is 0.02. We have to find the number of terms necessary so that the difference between the infinite summation and the sum of those terms differ by 0.00001.
This is what I did:
(U1 - r) / (1-r) - (U1(rn-1)) / (r - 1) = 0.00001
I get: - 0.2n + 10 =...
This is not a homework question per say, but rather a question I have about a text I am reading. In the text, they have defined
\sum E_{n} Cos \left( \frac{2 \pi X_{n}}{\lambda} \right) = E Cos \phi
If this is the case, is it fair to say that
\sum E_{n} Sin \left( \frac{2 \pi...
Find the Fourier Series for f(x)=x^2 evaluate f(0) and show that the summation
\sum^{\infty}_{n=1}\frac{1}{(2n-1)^2}=\frac{\pi^2}{8}
The first part of this problem asked that I find a_{n} and b_{n}
Since x^2 is an even function b_n=0 and for a_n I got \frac{4(-1)^2}{n^2}
for a_0 I got...
Hello, i have been trying to solve a summation question for a while, and I'm not too much of an expert at the subject, so i couldn't figure it out. it is the sum of n/n! in which n takes the value from one to infinity. In other words, just 1/1! + 2/2! + 3/3! + 4/4!...
Well, firstly, does the...
Homework Statement
I have a function
f(x) = x^2/4 for |x|<π
I have the Fourier series of this function which is
and I need to prove that
The Attempt at a Solution
I tried to use dirichlet for x = 0 but I get -pi^2/3
how can i use gamultiobj or ga, I've input of (i, j) matrix and i want (i,j) output
i've equation to solve with ga
f = sumation from i to class[ sumation from j to rows(yij * log(pij)))]
how to solve with ga
fun f = funGa1(Pij,Yij,class,rows)
f = -...
Homework Statement
Summation of i(i + 1) (with i going from i = 2 to i = n-1) = n(n-1)(n=1) / 3
a. Write P(2). Is P(2) true?
b. Write P(k)
c. Write P(k+1)
d. Prove by mathematical induction that the formula holds true for all integers
n \geq 2
Homework Equations...
Hi everyone,
I have these warning solving summation:
*************************************************
In[1]: f[m_, n_] := 2 n + 3 m;
In[2]: g[m_, n_] := Sum[f[m, n], {m, 1, m, 2}, {n, n, 1}];
In[3]: g[1, 1]
During evaluation of In[3]:= Sum::itraw: Raw object 1 cannot be used as an...
Homework Statement
By differentiating the summation, show that ∂/∂b₀ ƒ(b₀ , b₁) = -2 ∑_(i=1)^n (y₁ - b₀ - b₁x₁)
Homework Equations
the ‘derivative of the sums’ equals ‘the sum of the derivatives’:
The Attempt at a Solution
How would we partially differentiate a summation...
Hello,
could anyone give me a hint on how to find a closed-form expression for the following summation:
Q_N = \sum_{z=1}^N z^2
where z are positive integers from 1 to N.
Thanks.
Homework Statement
sum ((x-1)^(2n-2))/((2n-1)!) n=1..infinity?
after doing the ratio test, i found that the radius is from negative infinity to infinity (converges for all x).
is this right?
if not can you steer me in the right direction, please.
Homework Equations
The Attempt...
I posted this initially in Pre-Calculus, but, seeing several people with similar doubts have posted this question here, I'll do the same, even though I haven't started Calculus
I am investigating the sum of infinite sequences.
such that: t0 = 1 and tn = (x ln (a))n/n!
They tell me to...
I am investigating the sum of infinite sequences.
such that: t0 = 1 and tn = (x ln (a))n/n!
They tell me to first consider the following sequences of terms:
1, (ln 2)/1, (ln 2)2/2x1, (ln 2)3/3x2x1
They then ask me to calculate the sum Sn of the first n terms of the sequence for when...
Homework Statement
Prove\; that\;if\;\sum_{n=1}^{\infty} a_n \;converges,\;then \lim_{n\to\infty}a_n = 0
Book solution
s_n= a_1 + a_2 +...+a_n
s_{n-1}= a_1 + a_2 +...+a_{n-1}
a_n=s_n-s_{n-1}
Then they did a few limits, and proved that the difference is 0. BUt that is not my...
Homework Statement
Find the limit n to Infinity of summation (i=1 to n) 1/n * ((i/n)^2)
The Attempt at a Solution
I thought it was zero at first because 1/n goes to zero but apparently that's not right. I also tried to convert to an integral and got integral of i^2/n^2 which equals...
Does
\displaystyle S^2_X = \sum^n_{i=1} (X_i - \overline{X})^2
mean
\displaystyle S_X = \sum^n_{i=1} (X_i - \overline{X}) (X is a random variable here)
and is this true of summations in general?
i.e. does \sqrt{\sum X_i^2} = \sum X_i ?
I thought it'd be \sqrt{\left( \sum...
Homework Statement
Determine the value of the sum
\sum_{n=1}^\infty \frac{(-1)^n}{1+n^2}
I have determined it trough the use of Fourier series, but does there exist another way to do it?
Find the convergent sum and find the sum of first five terms
\sum_{n=1}^{\infty} \frac{sin(nx)}{2^nn}
from 1 to infinity.
I have found so far that:
\sum_{n=1}^{\infty} \frac{sin(nx)}{2^n} = \frac{2sin(x)}{5-4cos(x)}
I am not sure how to consider the \frac{1}{n} term.
Can someone please help?
I'm trying to find the partial derivative of Q with respect to w0 and then set it equal to 0 and solve for w0. Finding the partial derivative was easy, but once I've got it, I'm having a hard time getting w0 by itself. Here's the original equation:
Q(w_{0},w_{1},w_{2},w_{3})=\sum\left(y_{i}...
We solve Poisson's equation in cartesian coords for a region bounded by planes forming a box. Some of the planes are grounded. The lengths of the box are L1, L2, L3. There is no charge distribution.
Let a=mPi/L2
b=nPi/L3
The solutions goes like: sinh(sqrt(a^2 +...
When converting a summation of the form
\sum x_i y_i
to integration, how do we know if it's
\int x dy
or
\int y dx
At first I thought they're equivalent but obviously that's only true for a linear function with no constant offset.
I kind of see integration as a better...
Homework Statement
Given that \left(2r + 1\right)^{3} - \left(2r - 1\right)^{3} = 24r^{2} + 2,
show that \sum r^{2} = \frac{1}{6}n(n+1)(2n+1).
Homework Equations
No idea!
The Attempt at a Solution
Homework Statement
Prove that the following is true:
n
\Sigma lg k = \Theta (n lgn)
k=1
Homework Equations
the lg in this case is base 2
The Attempt at a Solution
i don't kno how to apply geometric or arithmetic progression to the 1st part
i was trying to substitute for k but that wasnt...
Homework Statement
My question involves the mid-point in deriving some of the equations to solve Laplace's equation in rectangular coordinates. The question may no make sense as it isn't problem specific. I can provide boundary values if necessary - just let me know.
Homework Equations...