# demonstration

1. ### Demonstration by Induction

Hi, I've been trying to demonstrate this(Worried): I know that $d_1=1, d_2=10, d_3=50, d_4=248$ and for $n \geq 5 ,d_n = 5d_{n-1} - 4d_{n-4}$. Demonstrate for all $n \in \mathbb{N}$ that: $$P(n): d_n < n \cdot 3^{n+1}.$$ I need to demostre this using the induction principle. My doubt is...
2. ### demonstration with discrete random variable

I would like to know if anybody from this forum have some insights about how to handle this demonstration: "Show that for any discrete random variable X, etE[X] <= E[etX], where t is fixed and belongs to R." (E is expected value) Maybe this is related with Jansen inequality, but certainly I'm...
3. ### Congruent Triangles Demonstration

Here is the following demonstration: In the figure PQ=QR, Angle 3 = Angle 4. Show that triangles PQS and PRT are congruent. I have tried several things here but none seem to work. I know that triangle PQR is isosceles. But that tells me that Angle P is equal to Angle R. From the figure it is...
4. ### Archimedes experiment \ show \ demonstration of double circular cone.

Can you tell me the relative angles that are needed for a double circular cone to climb up a slope? Far more interested I am at getting the equations and the whole procedure of finding these angles. A demonstration of which you can see here https://www.youtube.com/watch?v=yD4P1zN43zw Thank...
5. ### Demonstration envolving Complex numbers!! Help please

Please someone help me.. I've an exam in 2 days ... The following problem makes me nuts.. I can't get it right.. Show that: cos(∏ - alpha) + i cos (∏/2 - alpha) -------------------------------------------- = cis (∏ - 2alpha) cis (alpha) I'm desperate... I've tried everything I know.. any...
6. ### A simple Demonstration...

Hi, I've a problem with a (I know it must be very easy but I don't get it) demonstration about matrices... The thing I've to show is... Let A be a square matrix such as for all B (With the same order as A) AB=0. Then A=0. I don't wanna prove that there are no zero divisors in this ring...
7. ### Matrix little demonstration

Hello, I'm a bit bloqued on a little demontration. A^4=0 , (I-A)^-1 = I²+A+A²+A³ Here is what i've done: I=(I-A).(I²+AI+A²I+A³I) => I=I³+AI²+A²I²+A³I³-AI²-A²I-A³I-(A^4)I => I=I+A²+A³-A²-A³-A^4 => I=I-A^4 => A^4=0 But it is prove in reverse... The right way: If you know that...
8. ### (Very hard) Need help to solve a real-life problem that requires a "demonstration"

Please help me solve this situation or point me in the right direction. (please bear with my poor english) There are n candidates to be placed in n job positions. Each candidate selects 3 positions wich are ordered according to his/her preference. * Candidate cannot change this order * Each...
9. ### Demonstration Video: Handwriting recognition for maths!!!

Hi, This will be the last time I bother you with this for a little while. I have produced a rather amateur video (4min) of what I think handwriting recognition for maths should look like. For the time being, I have named it MathPen. http://users.ecs.soton.ac.uk/cmml100/VIDEO0012.mp4 What I...
10. ### Demonstration using congruency modulo m

Well, i am stuck with a problem. I have to prove that 7|(3^(2n+1) + 2^(n+2)) using the modulo m congruency. Well this will mean that 3^(2n+1) + 2(n+2) mod 7 = 0, but i cant find a whay to prove the initial expression. Any ideeas? Thanks
11. ### Simple Demonstration Exercise

Please help! Given: y'(t) + a(t).y(t) = f(t), with "a" and "f" continuos in R a(t) >= c > 0 lim (t->oo) f(t) = 0 Demonstrate: Any solution y(t), verifies lim (t->oo) y(t) = 0 Thank You.
12. ### inequality demonstration

There is this problem in my book: I just finished like 80 problems on solving linear, nonlinear, and absolute value inequalities, but I still can't seem to get the solution to this (presumably) simple problem. Could someone throw me a hint or two?
13. ### Demonstration for separation of variables

Hi there. I have to demonstrate that if an ordinary differential equation is susceptible to separation of variables, then its an exact differential equation. This is what I did: If it is separable then: g(y)dy=f(x)dx \rightarrow g(y)dy-f(x)dx=0 If and only if: \frac{\partial g}{\partial...
14. ### Demonstration 'reductio ad absurdum'.

Help me please with a demonstration 'reductio ad absurdum'! 1. - substitution - be a and b,two numbers greater or equal than 1 from the set of real numbers R, - be n a number greater or equal than 3 from the set of real numbers R, 2. - conclusion - there is always a and b...
15. ### Big O, little o demonstration

I must demonstrate that if \{ x_n \}, \{ y_n \} and \{ \alpha _n \} are sequences of real number then the following is true: if x_n=o( \alpha _n) then x_n=O(\alpha _n ). My attempt: I must show that knowing that \lim _{n \to \infty} \frac{x_n}{\alpha _n}=0 then there exist a constant C and an...
16. ### Demonstration of that the union of manifolds is not a mainfold

Hello. I was looking for that demonstration, and I know how to start: As they aren't contain in each other I have to take a point in each one that it is not in the other one. So they (the points) will be in the union of both of the mainfolds. So I have to proove that the half point of them is...
17. ### SOLVED Bessel functions recurrence formulas with demonstrations

Hi everyone. I have searched all over the internet how to prove recurrence formulas for Bessel functions, but I can't find it anywhere. So I decided to post here, for the first time on internet (?), the demonstrations of that formulas. Hope you enjoy :)
18. ### Demonstration involving sine and cosine

Hi there, I want to demonstrate that 1\leq{|\cos x|+|\sin x|\leq{\sqrt[]{2}}} How should I proceed? Bye and thanks.
19. ### Demonstration about matrices

Suppose that A and B are Hermitean and C and D are unitary matrices. Demonstrate that: 1)C^{-1}AC is Hermitean. 2)C^{-1}DC is unitary. 3)i(AB-BA) is Hermitean. My attempt for part 1) (I'll try to do the other parts alone). A Hermitean matrix A means that A=A^{\dagger} where the dagger...