0
votes
1answer
62 views

what is the coefficient of following expression

what is the co-efficient of $x^{50}$ in the expansion of $$\frac{1}{(1-x^{1.7})(1-x^{1.8})(1-x^{2.6})(1-x^{3.0})(1-x^{4.0})(1-x^{6.7})(1-x^{7.5})(1-x^{8.2})}$$ can you please explain me the logic
0
votes
1answer
44 views

Solving ODE with matrices

I have an equation in ODE $M{'}(x)= M(x)*A(x)$. Issue here is $A(x) = C_1+C_2* x $ where $C_1,C_2 $ has dimension $3 \times 3$. And x is a scalar variable Doubt What is M(x)? Can any one give ...
0
votes
2answers
26 views

Reliability Probability problem

What is the Probability that at least one close path is formed from A to B where each switch has a Probability of close = p and each switch acts independent of the other Proposed Solution Let ...
0
votes
0answers
22 views

Solution of definite integral of product of bessel function and exponential

I have an integral $I=\int_{\theta} \int_r J_m(k_1r)e^{-j[P_x r \cos(\theta)+P_y r \sin(\theta)]} r dr d\theta$ $0\leq\theta\leq2\pi; r<\infty$ is there any method to solve this?
2
votes
2answers
71 views

Solving the equation $n\log n = 10^9$

This seems very basic (I guess my calculus needs brushing up). Is there a way to find n without a calculator in this one? $10^{9} = n\log(n)$ My Attempt (log is base 2 base on the book convention.) ...
2
votes
1answer
85 views

First Order Logic Consistency Big Problem

as i read some tutorial material on First Order Logic, i deduce that the following formula was consistent in FOL except the third one. am i right? i have doubt about the first one. any idea? thanks to ...
3
votes
2answers
63 views

What am I doing wrong with this derivative? (Calculus)

I've been doing derivatives with the formula: Definition of a Derivative: for every $x$ plugin $(x+h)$, then subtract original from the equation. This means for $x^2$, I get: $$\frac{(x+h)^2 - ...
0
votes
1answer
88 views

Coin in City Problem [closed]

Please consider this problem. in one city common coin is 1dollar ,2dollar and 3dollar coin. how many way of paying the The price for an 20dollar candy which the seller has no money and number of ...
4
votes
5answers
323 views

Find a closed expression for a formula including summation

Let: $$\sum\limits_{k = 0}^n {k\left( {\matrix{ n \cr k \cr } } \right)} \cdot {4^{k - 1}} \cdot {3^{n - k}}$$ Find a closed formula (without summation). I think I should define this as a ...
1
vote
1answer
21 views

Cardinality of a set with a recurrence relation.

Let $A = \left\{ f\in \mathbb{N}\rightarrow \mathbb{C} \mid \forall n\in \mathbb{N}. f(n+3) + 3f(n+1) = f(n+2)+f(n) \right\}$ What is $\left|A\right|$? Well, I tried to treat $f$ as a recurrence ...
1
vote
1answer
46 views

I'm searching for the formula of the series $ \sum_{n=0}^{\infty}a^{n^l} $

I'm searching for the sum-formula (if exists) of the following power series: $$ \sum_{n=0}^{\infty}a^{n^l} $$ where $l=2,3,....$, and $|a|<1$.
1
vote
1answer
44 views

question application product

can any one help me in this questions The perimeter of a square is equal to four times the length of a side of the square. Find the perimeter of a square whose side $s$ measures $2.7$ meters? thank ...
1
vote
1answer
37 views

A naive example of discrete Fourier transformation

We know a discrete Fourier transformation with discrete $n$ and continuous $x_1,x_2$: $$ \sum_{n\in\mathbb{Z}} e^{-in(x_1-x_2)\frac{2\pi}{L}}=L\delta(x_1-x_2) $$ with Dirac delta function $\delta$. ...
0
votes
0answers
309 views

How can I derive the PDF from conditional probabilities?

I have some function $P(i)$ which is the probability of success for an experiment on the $i$th trial. The probability mass function for the first successful trial is: $$PMF(n) = \left( ...
0
votes
0answers
11 views

About the logistic map.

I need guide line about it I also wanted to know how it will appear in graph if we use mathematica or some other software for this.
1
vote
2answers
39 views

About Recurrence Relations.

I need help in order to solve the following question, Here RR is for Recurrence Relations.
0
votes
1answer
29 views

A question on discrete sequences

Suppose for $1 \leq n \leq M$, we have a discrete sequence $a_n = (1 - 2^{n-M}) \gamma^n$, where $M$ is a fixed strictly positive integer, and $\gamma$ is a fixed strictly positive real number such ...
0
votes
2answers
85 views

recursive algorithm for fibonacci numbers?

Trying to figure out if I would use a recursive algorithm for fibonacci numbers. My problem is "Devise a recursive algorithm to find the n-th term of the function defined by $f(0)=0, f(1)=1, f(n+1)= ...
1
vote
5answers
137 views

Proofs using Mathematical Induction

I have two problems that I am trying to solve using mathematical Induction but am confused on how to know when process to use. 1) Prove by mathematical induction that ...
1
vote
2answers
49 views

GCD of pairs of integers

So I think I am just psyching myself out right now and this is way to easy but I am running on no sleep in the past few days so forgive me please. The question is what are the greatest common divisors ...
0
votes
1answer
65 views

Proving using squeeze principle

This problem sounds very confusing. Please help me solve this problem.
0
votes
1answer
16 views

One to one function behaviour

Like in pigeon hole principle , if one set of objects(S1) has more items than others set of objects(S2) and we try to fit that S1 in S2 ( that is mapping the values of S1 to S2 , we end up getting ...
-1
votes
1answer
332 views

how to determine the largest n for which one can solve within one second using an algorithm

So I am confused on this problem for my discrete math class, I didn't know if there was a specific formula you were supposed to use or what. The question is "What is the largest n for which one can ...
0
votes
1answer
32 views

Least squares method: must each partial derivative be zero?

In gradient equations, does the sum of the partial derivatives have to be equal to zero or each derivatives has to be zero? As I have just started to understand gradient equations, if my question is ...
4
votes
1answer
66 views

What is the history of this theorem about the finite sum of a polynomial?

I discovered and proved the following theorem back in high school, and have waited patiently to hear something about throughout my college career (which is nearing it's end, hope to have finished my ...
0
votes
1answer
36 views

Logical form of this statement?

In logical form, how would you express : Take any two fractions, add them together, and the result will be an integer
3
votes
1answer
71 views

Solve difference equation

Fix a real number $a\not=0$. How to solve recursive equation $a_{n+1}+(2-na)a_n+a_{n-1}=0$. Even a solution for a prescribed value of $a$ should be fine.
4
votes
2answers
65 views

Newton iteration method

i need some help here. My function is $f(x) =x^{3}$ . I was asked to find the number of iterations that are needed to reach the precission $10^{-5}$ if $x_{0} = 0.9$ I was wondering if there is a ...
0
votes
0answers
32 views

Proving a DTFT relation

I'm trying to prove that the inverse DTFT of: $$\frac{1}{1-ae^{-j\Omega }} $$where |a|<1 is: $$a^{n}u[n]$$ The way to prove it is by the integral below but I'm not sure how to proceed: $$ ...
2
votes
1answer
61 views

How many integer solutions does $x_{1} + x_{2} + x_{3} = 14$ have ?, where $x_{1} , x_{2} \geq 0$ and $x_{3} > 2$.

How many integer solutions does $x_{1} + x_{2} + x_{3} = 14$ have ?, where $x_{1} , x_{2} \geq 0$ and $x_{3} > 2$. What should I do with this kind of problems ?. Thanks.
-1
votes
1answer
34 views

Which equation has a solution $(x,y)$ i which both $x$ and $y$ are integers?

Which equation has a solution $(x,y)$ in which both $x$ and $y$ are integers? $12x + 9y = 16$ $32 x + 80y = 27$ $42x + 56y = -28$ $20x + 90y = 105$ Do we have to use discriminant ($b^2 - 4ac)$ ...
0
votes
4answers
66 views

If $c$ is a positive real number, then the equation $2x^2 - 3x - c = 0$ has:

Multiple Choice: If $c$ is a positive real number, then the equation $2x^2 - 3x - c = 0$ has: (a) No Solutions (b) one solution (c) two solutions (d) three solutions Attempt: Can we assume $c$ to ...
2
votes
1answer
27 views

Ant problem with discrete combinatorical background.

an ant can move along a grid in $\mathbb{Z}^2$. But the ant can only go upwards and to the right(with equal probability). The ant starts in the point $(0,0)$, but there is an electrical wire from ...
1
vote
0answers
44 views

Noob Question about a discrete surface

I am looking for a nudge in the right direction as to how to solve this problem. I have data which defines a solid cylinder. The data is composed of a 3d internal radius and a thickness at each point ...
0
votes
0answers
23 views

Two dimention recursive recursive equation

I am unable to solve the following recursive equation which I must solve in my research problem. Please give me advice or solution to the problem. For $K=\min(N/2,C)$ and N,C T_c, T_s,p,T are ...
1
vote
1answer
112 views

What is the coef´Čücient of $x^7$ in $(1 + x)^{11}$?

What is the coefficient of $x^7$ in $(1 + x)^{11}$? I don't know how to solve this question please help me
0
votes
0answers
32 views

How to calculate the frequency of an array of timestamps?

How can i calculate the medium frequency of an event knowing the date and time of each time it happens. I have the data on unix timestamp: ...
2
votes
2answers
179 views

Meeting point for 5 people with least distance travelled (interview question)

I had an interview today and I'm completely stumped on what they asked me. Essentially: if you are given 5 people on a 2D grid, and you need to meet at a point with the least amount of distance ...
0
votes
1answer
65 views

Find permutation index of multiple lists where corresponding list indices match

I have several date time values: Mon 17h10 Tue 20h30 Wed 21h45 that maps to the following lists ...
3
votes
1answer
56 views

For $n \in \mathbb{N}$ how many times do I have to do this: $k=\lfloor \frac{n}{2} \rfloor$ till $k=1$?

For $n \in \mathbb{N}$ how many times do I have to do this: $k=\lfloor \frac{n}{2} \rfloor$ till $k=1$? For example $11 \Rightarrow 5 \Rightarrow 2 \Rightarrow 1$ And a bunch of other examples lead ...
-1
votes
3answers
113 views

Prove $2^n > 10n^2$ for all sufficiently large integers n.

How do I prove $2^n > 10n^2$ inductively? I know you can prove this to be true using calculus (i.e. taking derivatives). But how would I do it inductively?
1
vote
1answer
41 views

Invertible Functions

In some mathematics texts, a function is invertible iff the function is one-to-one and onto. However, in some calculus texts (thomas's calculus, stewart's calculus, etc.), the only requirement for a ...
1
vote
1answer
31 views

Knowing that $b\leq\frac{a}{1-a}$ and $a<0.01$ show that $b \leq 1.01a$

I've been solving a problem in numerical analysis and to finish one of the exercises I need the following result. Knowing that $b\leq\frac{a}{1-a}$ and $a<0.01$ show that $b \leq 1.01a$. Now I ...
0
votes
1answer
86 views

How many solutions are there to this equation involving the floor function: $(n+1)x-\lfloor nx \rfloor = c$?

How many solutions are there for this equation: $(n+1)x-\lfloor nx \rfloor = c$ I can prove some basic properties of floors and ceiling, but here I'm stumped.
0
votes
0answers
17 views

Add user in Center collection

I am working on a software which does the work basically counting points of user and generating scoreboard using some formula given below. It has got 2 paramaters x, y; ie, each user is assigned two ...
0
votes
4answers
112 views

Proof of continuity [closed]

Let $$f:\mathbb{R}\mapsto \mathbb{R}.$$ Prove that if f is differentiable at a real number c, then f is continuous at c.
0
votes
1answer
101 views

How do I find the probability of these three events?

Sample space is all houses in zip code 80210. Event A is that the houses were built in 2002, event B is that the houses have 3-car garages, and event C is that the houses have lead-base paint. ...
2
votes
0answers
40 views

getting PDF from a given Moment Generating Function

if the moment generating function mgf of a random variable w is M(t)=(1-7t)-20 find the i)pdf ii)mean iii)variance of w
0
votes
1answer
107 views

How to solve this minimization (maximization)?

I'm facing this problem: $$ \large \min_{x \in \mathbb{R}_+^3} \max \left\{ { \sum_{i=1}^3 x_i^2-2 x_1 x_3 \over \left(\sum_{i=1}^3 x_i \right)^2} , { \sum_{i=1}^3 x_i^2 + 2 (x_1 x_3 - ...
8
votes
2answers
200 views

How find that $\left(\frac{x}{1-x^2}+\frac{3x^3}{1-x^6}+\frac{5x^5}{1-x^{10}}+\frac{7x^7}{1-x^{14}}+\cdots\right)^2=\sum_{i=0}^{\infty}a_{i}x^i$

let $$\left(\dfrac{x}{1-x^2}+\dfrac{3x^3}{1-x^6}+\dfrac{5x^5}{1-x^{10}}+\dfrac{7x^7}{1-x^{14}}+\cdots\right)^2=\sum_{i=0}^{\infty}a_{i}x^i$$ How find the $a_{2^n}=?$ my idea:let ...