Mathematics

how to show this: if f(x) = 2x/(2x-1) then show f(n) + f(n)f(n-1) + f(n)f(n-1)f(n-2) + ... + f(n)f(n-1)f(n-2)...f(1) = 2n . I have tried to use induction , and I can show it. but , I can't show it without using induction. can anyone tell how to show it without using induction? thank you !

For what reason, the induction only can be used to prove natural numbers n(but not negative numbers?)? How to guess the formula of a sum of a sequence of number?

Hi again...This is my last question for today. I know that i send a lot of threads but...i dont have anyone else to help me. Most of the times i dont send any solutions.I try but sometimes i dont understand and so...i dont have something to write.I post frequently because if i dont give a 50% of correct answers i will not have the chance to write in the final exams...its a stupid rule. My last 2 questions for today are. 1.We must prove that if P(A/B)=1 then P(B compl. / A compl.)=1 i wrote a lot of things but ..i didnt prove nothing : ~) 2.A and B are two events with non zero probabilities. I must show (prove) if the following are i)correct,ii)faulse …

Hi guys i know that i post a problem without my own answer but this problem is very difficult for me and i'm very comfused. The exercise says that we must implement the Bayes' Law to solve the exercise.My problem is that i cant distinguish and write down the events ): Problem:In my kitchen i put my 10 forks in the left drawer and my 10 knifes in the right drawer. before my room mate change something: k=knife,f=forks left drawer : (10f,0k) right drawer: (0f,10k)) When my room-mate came he took 2 forks from the left drawer and he put them in the right drawer. after my room mate's alteration: left drawer : (8f,0k) right drawer: (2f,10k) After this action …

Hi...Can you plz check if my proof is correct? Exercise: A1,A2,.....An are independently events. Prove that : P(A1[union]A2[union]...[union]An) = 1-Πi[element-of]I(1-P(Ai)) note for this (Πi[element-of]I(1-P(Ai)) I={1,2,....n) P([intersect]Ai)= Π P(Ai) for 3 events A1,A2,A3 means: P(A1[intersect]A2)=P(A1)*P(A2) P(A2[intersect]A3)=P(A2)*P(A3) P(A2[intersect]A3)=P(A2)*P(A3) P(A1[intersect]A2[intersect]A3)=P(A1)* P(A2) * P(A3) Now my proof: We know that P([intersect]Ai)= Π P(Ai) if A1,A2,...,An are independent then and the complements are independent P([intersect]Ai)complement = Π P(Aicomplement) P([union](Ai compl) ) = Π(1-P(Ai)…

a line of 100 airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. (for convenience, let's say that the nth passenger in line has a ticket for the seat number n.) unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. all of the other passengers are quite normal, and will go to their proper seat unless it is already occupied. if it is occupied, they will then find a free seat to sit in, at random. what is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?

I believe that there should be a standard list of theorems (#1-#144(?). It is very confusing talking to someone with a different textbook, and referring to theorem #1, when yours is something like "all right angles are congruent", and his is, "If a radius is perpendicular to a chord, then it bisects a chord". I propose that a universal set of numbered theorems should be established to reduce confusion and help unify mathmatics. Anyone disagree or, agree?

A non technical explanation of Monadic Mathematics' '+' and '-' operations Let me explain my framework without technical formal definitions. Monadic Mathematics exists between two opposites which are its limitations. By limitations I mean that it cannot work beyond these opposites. The opposites are Emptiness (which is notated as {}) and Fullness (which is notated as {__}). {} or {__} cannot be used as inputs in Monadic Mathematics framework. Let us call Monadic Mathematics MM. The fundamental concepts that are used in MM are Length, Direction, Quantity. If we examine R from MM point of view, then we get this picture: Each number is…

Im not posting this in the physics forum because i feel its more of a amth question. My friends and i have bulit an air cannon and i wish to analysis it mathematically...after a couple of hours i came up with an equation i think would do. I was wondering if people could look at my work and see of they see anything wrong with it. First off my aircannon has a simple chamber then a valve and then a barrel. You pump air in to the camber and then let relase the valve and then the projectile is shot(ps i have never used LaTex before so we will see how this goes) first off i started with the equation [math] p=\frac{F}{A}[/math] In this problem i am going to assume the …

anyone know the syntax for soloving a systems of eqs? I forgot what is was and cant re-figure it out...i know its somethng like solve(f(x,y)=a; or , f(x,y)=b, or ; (a,b)) or smoething like that for example a + b = 2 3a + b^2 = 8 just pull out of my head for the syntax purposes

Can anyone solve this proof? Given: M is the midpoint of AB; <1 congruent <2; <3 congruent <4 Prove: AC congruent BD Desperate! I need quick answers!

A rational function is the ratio of two polynomial functions. If P(x) and Q(x) are polynomials, then a function of the form R(x) = P(x)/Q(x) is a rational funcation where Q(x) not equal to zero. The domain R(x) is the intersection of the domain of P(x) and Q(x). How is this done, can someone elaborate on the idea of graphing rational functions?i also read that under certain conditions, like Q(x)=0 and P(x)!=0, etc, the graphs formed are Vertical Asymptotes or Horizontal Asymptotes. I could not understand them.

Can a number in of itself hold certain powers?

okay i have recently become intrested in iterative functions and im trying to solve the family of equations [math]x_{y+1}->x_y^n+c[/math]...k so using my calculator i graphed the equations i found some compelling results(btw trying to solve algebratically is tedious i belive it would be impossible tofind its limit)the y axes i set as the value the function converges too and x axes a value of c and i set x0 to zero i found that the functions stick to the function y=x and then suddenlystart to diverge from it,but as n increases the graph stay more and moreon y=x so my conjecture is that as n->infinity [math]x_{y+1}->x_y^n+c[/math] becomes the graph y=x through an i…

Hi guys i have a problem but i dont know how to start solving this can you help? We have three events: A={The midday temperature in Hirakleio is 25C} B={The midday temperature in Athens is 25C} C={The maximum of the two midday temperatures in Hirakleio and Athens is 25[degrees]C} P(A)=0.3 P(B)=0.4 P©=0.2 Find the probability that the minimum temperature between the two midday temperatures is 25C

Absolute Infinity was "conceived" or lets say discovered by Georg Cantor and was considered to transcend all the transfinite numbers and the the set of all sets (paradox). But there was never any explanation to why there couldnt be an end to numbers, to humans, to whoever. Now this might sound like a stupid thread, i might be given explanations "because it just goes on and on and on" well that is true but we couldnt reach Absolute Infinity just by going on and on. Why arent the line of numbers with a start and an endpoint but the "space" of numbers in between the start and end is continuously infinite, transfinite, or Absolutely Infinite? Why isnt there a "Totality" that …

Hi.. I have an exercise and i want to know if i solved it correct.Can you help? Three people A,B,C throw a coin (First is A,second comes B and finally C) The first that will bring head wins and the game stops. The exercise wants: a)The sample space b)Determinate the following events in the sample space i)A={A WINS} ii)B={B WINS) iii)(A union B)complement H:HEAD T:TAIL a)sample space{H,TH,TTH,TTT} bi)P(A)={H}=1/2 bii)P(B)={TH}=P(Acomplement intersection B)=1/4 biii)(A union B)complement=Acomplement intersection Bcomplement= {TTH,TTH}=1/4 is it corrent?

In this link http://www.geocities.com/complementarytheory/GaloisDialog.pdf you can find a dialog between 3 persons (one of them is me) discussing about the foundations of the language of Mathematics in a new light. I'll be glad to get any detailed opinion on this dialog, thank you.

I would just like to state that the concept of Infinity does not actually exist, it is merely a device fabricated by the mind's inability to grasp the size of the universe. Everything is finite even Pi and the Universe. We havent found the end yet because our computers are made to think in terms of infinity. Time is a similar device, simply another device made by man to aid in the understanding of the 4 dimensions respectively.... Furthermore , the human race is one of pompous beings, how could anyone of us have the gall to truly believe that we are infact at the top of the genetic roster?! Please respond with any words that you would like, we are having trouble..

I'm assuming this is the proper forum to post this in, even though I'm asking rather than testing whether anyone knows the answer to this (because I don't). Does anyone know how to solve [math]a_{n+1}=e^{a_{n}}[/math] explicitly for [math]a_{n}[/math] in terms of [math]n[/math] and [math]a_{0}[/math]? I would greatly appreciate knowing both the solution and the method used to obtain it, since my own studies have taken me where a solution would be extremely helpful. I haven't been able to determine whether this is a simple textbook equation or a problem entirely unsolved by the mathematical community.

There is an article in New Scientist about it but no article on there site. found some other link about it here: http://www.math.uwaterloo.ca/navigation/ideas/grains/pi.shtml It's not news but I didn't hear that before but it's sure interesting.

The recent thread e^x=x has gotten me intressted in what it roots are. Through my look at it i think there is a infintude of roots...let me explain one root is very easy to get take the root of x on both sides and you get e=x^1/x which you can easily solve with newtons method setting x0->i but on further anaylsis e^(a+bi)=a+bi a+bi=ln(a+bi) take the polar a+bi=ln((a^2+b^2)^(1/2)cis(arctan(b/a)) set it to exponetial a+bi=ln((a^2+b^2)^(1/2)e^(arctan(b/a)*i)) reduce down and you get a+bi=ln(a^2+b^2)/2+arctan(b/a)*i now because of the periodicness of arctan there should be an infinte # of solutions i belive but i dont know how to solve for them....wait i just re…

Do they really exist? I once saw a proof showing that they were the same as positive numbers. I think it may have come from Dave. I will try to look for it. If negative numbers are the same as positive, does that mean imaginary numbers are just a fabrication of man?

I know what Radians and Degrees are, but what are Grads?

hello guys! i have a column with a shape of a cylinder. the radius is 2cm and the heigh is 5cm. i have to calculate the cross-sectional area of the column. i wonder what is the formula and how is the calculation? it has been a long time since i last had my math lectures, so i really hope for some help! thanks alot!