Mathematics

Let a,b, and c be positive real numbers. Prove that [math]\sqrt{\frac {a}{a+b}}+ \sqrt{\frac {b}{b+c}}+ \sqrt{\frac {c}{c+a}} \leq 2\sqrt{1+\frac {abc}{(a+b)(b+c)(c+a)}}[/math] I've tried squaring both sides, and that eventually lead me to nothing. Then I tried taking the common denominator of the left side, but I got nothing either... There has to be some trick involved that I'm not seeing... Anyone has any suggestions or input, that will be great!

Interpolate them.

During preparations for a mathematical contest I might take part in, I've come across an interesting problem: Let [math] n \in \mathbb{N}[/math] and [math]a, b \in \mathbb{Z}[/math] be integers such that the set [math]\mathbb{Z} \setminus \{ ax^n+by^n, x, y \in \mathbb{Z} \}[/math] is finite. Prove that n = 1. The "official" solution is the ugliest thing I've ever seen, and so incomprehensible that even my professors didn't understand it. My gut was/is telling me that there was a simpler solution, so I've been trying to find one. I've gotten to the point where all I have to do is prove that the set [math]\mathbb{Z} \setminus \{ x^{2k+1}+y^{2k+1}, x, y \in \mathb…

I've searched on wikipedia and wolfram mathworld, and i have a definiton on a book right in front of me: After that there are some properties. But I still can't understand it. Can you help me? Thanks in advance.

My interest in math is not only philosophical but as metaphors that may inspire me as an engineer as well.

Find the summation of: [math] \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n} (1-\frac{1}{2}+\frac{1}{3}-...+\frac{(-1)^{n+1}}{n}) [/math] We know this is an alternating harmonic series if we look at the first part is just [math] \sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n} [/math] and multiplied to the second part which is [math] \sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n} [/math], this is also another alternating harmonic series. So the product of these two should converge to ln(2) for each part right? But I don't know how to show how they converge... so the summation is just (ln(2))^2? Or another way I looked at it is, distributing... [math] \sum_{n=1}^{\infty} (1\fra…

Gotta click through the hyperlink in link removed to get to my explanation of Bayesian logic.

How is this represented?

what do i do here ?

I need to present rounded numbers in my software. For example, after calculating "sqrt(2)", the software could display the result as: "1.414" (it only shows the result to a 'reasonable' precision). How to mark this number as a round-off number? Is there a standard notation in mathematics? From the displayed value it should be immediately visible if the result is rounded or exact. For example, consider the following two cases: 1/8 = 0.125 (the exact value) sqrt(2) = 1.414 (rounded value) If there is no standard way to somehow mark numbers that are rounded, I was thinking to put a dash under (or over) the last digit. Or maybe printing out the last digi…

i have three months to study everything in the "heading " where should i start .. my whole life is depending on this crap .. seriously .. help ...

ok so if we say that a is a natural number (N) this (a+30)(a+50)(a+70) what can it be divided by? 2, 3, 5, 7? which one(help plz, btw soz maybe its bad math lang)

derivative (outer function ) (whole terms) * derivative (inner function) ?

getting lots of stuck from this algebraic expression ?? 1. The problem statement, all variables and given/known data (4x−1)1/2−1/3(4x−1)3/2 2. Relevant equations 3. The attempt at a solution I think the GCF is (4x−1)1/2 . So, I get (4x−1)1/2(1+(−1/3(4x−1))) = (4x−1)1/2(−4/3x+4/3) = −4/3(4x−1)1/2(x−1) However, the answer in the book is 4/3(4x−1)1/2(x−1) . I've done it several ways, and I either get a minus sign on the 4/3 , or the (x−1) becomes (x+1) . What am I missing?

Good day. I was working on my set theory home assignment when I found out that I got no useful knowledge on how to construct proofs. I all ready have tried reading about proofs and making sure I can read simple proofs (As should be the one I need to construct) but now I have understanding that I do not have any real understanding about what proof exactly is nor how it should be formally constructed. That is the reason I am here. I would like to get some tips and ideas on how to understand proof and help on working my way to create proofs. PS, I am a University 1-st year student and actually have really bad math background. Also, I have been working on elect…

1^∞ ≠ 1? What, Is this really indeterminate? 1 * 1 * ... * 1 = 1 1 * 1 = 1 = a a * 1 = 1 = a edit: I misunderstood "indeterminate"

Here is a question to think about. We assume that any element of a set with cardinality A, when represented by symbols, must have less than or equal to A symbols, which I think is a fair assumption. The real numbers have cardinality C. So any number in the set of reals, when represented by, whatever, 0's and 1's if you wish, can have at most C of these objects to represent it. The cardinality of the power set of the reals, is 2^C>C. Now, we can imagine a number who has 2^C symbols to represent it. This number is technically not in the reals, since it must be of a set with cardinality greater than the reals. But this number is what we would intuitively think of …

hello everyone i need some help am not good in mathematics so if any one can help i need books or software to help me and i will be grateful

p(x)=a1x1+a2x2+......anxn is a polynomial if the polynomial is divisible by x+c where c is real number we get; p(x)= q(x).(x+c) x+c=0 x=-c if plug that in to the division we get; q(x).(x+c)/(x+c) p(x)= 0/0 although this is a clear contradiction, why is it still possible to use it in mathematical calculations and give us right answer??? sincerely yours;

As everybody knows, the infinity is a term that can never be reached and defined in our current mathematics system. But as you may know,all our mathematic theories must obey the laws of the universe.As it is accepted by many physicians that the begining of our universe started with the big bang ,where the universe started to have a volume and a mass.As it is also known the fastest moving thing in the universe is the speed of light. Even though the universe is expanding, at the current time, it has a certain volume with certain borders. So at the current time ,lets say the given time is T(n) Lets define the time where the big bang happened and everything start…

I'm reading the book "The rubato music composer" and on fourth chapter, he says i need a basic knowledge about set theory. What are the pre-requisites for learning set theory? And is there a consense of what this basic knowledge may be?

Are there any alternative computing engine of WolframAlpha?

1/(1/0)=? (not limit) Is it zero or undetermined?

The current mathematics is limited and sinful. I'll show you the six examples, who I am, present a review of mathematics 1. trisection angle image.1. OA ruler - along image.2. caliper O-OA- circular arc image.3. caliper A-AO-I walk a circular arc to get the point A1 image.4. OA1 ruler - along image.5. caliper A1-A1A - get round image.6. caliper A-AA1 - get the second round, we get the point B at the intersection of two circles image.7. OB ruler - along, I walk AA1 circular arc, we get the point A2 this process with a ruler and compass (angle bisection) is a set of numbers listed in the picture (infinite , image 8 ) We have been the angle of the picture that…

This is work I have been working on Primes. I just want to know what people that know a little about math think. (They can appreciate it more than not knowing a little trig.) Here it is check it out and let me know what you think. http://www.constructorscorner.com/ideas_and_gadgets/math/math_hunch/hunch_00001/just_a_hunch/prime_theory002.htm