Binomial Definition and 640 Threads

I was going the derivations for Fresnel zone radius approximation, and there was a jump in the math which I don't fully understand. If someone could take a look at this and help me figure. I was hinted that it had to do with the binomial theorem, but I have no idea >.< Seems like LaTeX isn't...

What is binomial expansion?

could anyone explain binomial expansion in the simplest way?

k, maybe wrong forum... whatever... Anyway, so i was hoping someone could maybe derive or at least explain binomial coefficients. Like, i know that binomial(n,r)= n!/(n-r)!r! but why? in class the guy was explaining something like, if you're counting, and you're trying to arrange 3 balls into...

I am trying to do a question from Eugene Hecht's Optics book, which goes something like this: Given the following equations: Cauchy's Equation: n = C_1 + \frac{C_2}{\lambda^2} + \frac{C_3}{\lambda^4} + ... Sellmeier's Equation: n^2 = 1 + \sum_{j}...

Okay, well, perhaps I am already done, perhaps not. This is why I seek your wisdom :) If you are asked to find the first 5 terms of the expansion (1 + 0.07)^9 using the Binomial Theorem, and then asked to use these terms to estimate the value of 1.07^9 what would you put? I added the 5...

I am working through a mathematics olympiad problem book, and I am asked to prove that n choose r, where n is the row number and r is the term number in the row is equal to that term. Can someone please give me a hint? I have not been able to find ANY proofs on the internet through a basic...

Find the term containing x^{20} in (2x - x^4)^{14}. I went t_{k+1}= _{14}C_{k}(2x)^{14-k}(-x^{4})^{k} = 2x^{14-k}(-x^{4k}) First of all, am I on the right track? If so what exactly do I do from there?

hello all I thought this might be an interesting question to ask, consider the following series \sum_{n=0}^{\infty}\left(\begin{array}{cc}\alpha\\n \end{array}\right)x^{n}=(1+x)^{\alpha} this is known as the binomial series, what's confusing me is that how could this series exist when...

Hello Guys, I just have a few quick question on binomial theorem, any help would be greatly appreciated. 1. Expand using the binomial theorm in powers of x up to and including x^3 : (1 + 2x + 3x^2)^5 : I always thought binomial theorm would be used to expand binomials... this is not a...

It seems like this shouldn't be too difficult and yet I'm stumped. I am trying to prove the binomial theorem. (x+y)^n = the sum from k=0 to n of (x^k)*(y^n-k)*(The binomial coefficient n,k) Sorry, about the notation... Anyway, I figure the best way to go about proving this is by...

I have a bag of M&M's that is 22.5% Blue, 12.5%Brown, and 65% other. If I pull 12 M&M's from the bag, what is the probabiliity that exactly 2 are blue and 3 are brown? I used the binomial to find the probability of 2 blue and 3 brown, and I want to multiply them together to get the answer...

Hi! I haven't found any good proofs of the binomial theroem. But I've discovered how to go from (a+1)= bla bla to (a+b) = bla bla. So if anyone could told me how to prove (a+1) = bla bla...

The questions are as follows 1) How many terms are there in the expansion of (a+3b-2c-d)^8 before like terms are combined? 4^8 2) How many terms are there after like terms are combined? _8C_4=70 3) What is the coefficent of a^2b^3cd^2? (_8C_2)( _6C_3)( _3C_1)( _2C_2)...

Hi, I'm having some problems with this question - Find the term independent of x in (x^2 - 2/x)^6 I know the answer is something like 6Csomething 2^something, but I'm not sure how to get that. So far I've only really done simple things like (x+y)^n where y is an integer and not...

Can Someone Plz Answer Asap! My teacher gave me homework and i got to convert for ex. (a+b)squared=a squared+ab+b squared, i got to do this up until to the 15th power. Please anyone have an ez way to do this or a shortcut. PLZ REPLY MY SPRING BREAK IS ALMOST OVER I HAVE LIKE 3 DAYS TO DO THIS

For a binomial distribution with n=10 and p=0.5 ,we should not use the poisson approximation because both of the conditions n>=100 and np<=10 are not satisfied. SUppose we go way out on a limb and use the Poisson aproximation anyway. Are the resulting probabilities unacceptable...

I've been struggling with this problem for hours. I don't know what I did was wrong. Someone please give me a hint or point out where I did was wrong. Thanks a lot. There are three charges : the first charge of +2Q locates at (0,0), the second charge of -Q locates at (0,d), the third charge...

Is this a good problem: Which is a better model for valuing American options: the binomial or the Black Scholes? Any feedback is appreciated Thanks :smile: ps: sorry for the hiatus

I've got 1 question regarding the binomial series which I am currently stuck at. 1. Expand (1-x)^-^3 and express the coefficient of x^r in terms of r. What i did was to first expand it, according to the binomial series, and I got, 1+3x+6x^2...\frac {(-3)(-3-1)...(-3-r+1)}{r!}...

Find the coefficient of the term X^5 of the expansion (3x^3 - \frac{1}{x^2})^{10} Another question off the topic. Find the x-coordinate of the minimium point of y=2x^2-5x+3 I know I have to complete the square but I'm not sure how its done.

I'm working on an IB mathematics portfolio, and here's a problem I don't understand: It's not specified what a and b is supposed to represent. That's where I need some explanation. I already made a nice Pascal triangle all the way to the 10th row. All help is appreciated.

How do you expand and simplify (1 + \sqrt\frac{2}{n-1})^n? I know this involves a binomial expansion and I can expand it to look something like \left(\begin{array}{c}n&0\end{array}\right){\frac{2}{n-1}}^\frac{0}{2} + \left(\begin{array}{c}n&1\end{array}\right){\frac{2}{n-1}}^\frac{1}{2} +...

could someone please shed some light upon the following dilemma: Given that D~B(12,0.7), calculate the smallest value of d such that P(D>d) <0.90. much obliged

I have my question and my problem in the attachment that followed.

I have my question and my problem in the attachment that followed.

Binomial Theorem... Hi I need to know about binomial theorem... eg. how to in general expand (a+b)^n I don't understand the combinations / permutations...? thanks Roger

the inverse of 1/(2x+6) x cannot=-3 is -3 + 1/2x ? Is this correct?

Hey. I am having difficultly with two math problems: 1. In the expansion of (mx+n)^5 the numerical coefficient of the second term is -48 and of the third term if 28.8 Find the values of m and n. 2. The first three terms in the expansion of (1+a)^n are 1-18+144. Determine the values of...

(a) Expand f(x)=\frac{x+x^2}{\left( 1-x\right) ^3} as a power series. (b) Use part (a) to find the sum of the series \sum _{n=0} ^{\infty} \frac{n^2}{2^n} \hline Here is what I've got: (a) f(x)=\frac{x+x^2}{\left( 1-x \right) ^3 } = \left( x + x^2 \right) \left[ 1...

In a series of three binomial trials with p=.4, a random variable, X, is assigned to the outcomes to form a base 2 number, with 1 associated with success(S), and 0 associated with failure(F). For example, SFS->101=5. A) Find the expected value of X, E[X]. (Answer 2.80) B) Find the...

binomial distribution Prob of rolling a 1 = 1/10, rolling a 2 = 2/10, 3 = 3/10, 4 = 4/10 Let X be the value thrown Calculate E(X) and Var(X) To do this can't use E(X) = np and can't use Var(X) = npq is this correct?

Hi, I've spent dozen of hours searching by my-self and dozen of hours searching on the Web. Now I need help. Who could provide a proof for this binomial property ? I need it for another proof. Thanks Tony Let: F_n=2^{2^n}+1 , n \geq 2 . Prove: F_n \text{ prime } \Longrightarrow F_n...

Binomial Expansion problems!Please help me ASAP! 1)Using binomial expand (3X +4)^4.can you please kindly explain your process. 2)Use the first 4 terms in the binomial expansion of (3x+4)^4 in the DESCENDING order of x to determine the approx. of 1.004^12.Can you please give me the way how to...

Hi guys, if you can help me with this problem it would be of great help 1) Pythag-Air-US Airlines has determined that 5% of its customers do not show up for their flights. If a passenger is bumped off a flight because of overbooking, the airline pays the customer $200. What is the expected...

I get a number that is too big when I calculate the coefficient of x^25 in: (2x - (3/x^2))^58 This is how I found the coefficient: Note that (58) = A combination value... k (58) * (2x)^(58-k) * (-3/x^2)^k k (58) * (2)^(58 - k) * (x)^(58 - k) * (-3)^k * (1/x^2)^k k...

I need help with 2 series problems: http://fantasyland.250free.com/Series.jpg I was able to solve part a, but I don't understand part b or part c. http://fantasyland.250free.com/binomial_relativity.jpg I don't get this one at all. Any help would be appreicated.

Hi, I am having a little trouble with this proof: Let n be a positive integer. What is the largest binomial coefficient C(n,r) where r is a nonnegative integer less than or equal to n? Prove your answer is correct. So let r = \lfloor{\frac{n}{2}\rfloor} or r = \lceil{\frac{n}{2}\rceil}...

What sort of distribution (eg binomial, normal..) would you expect each of the following to be? I am trying to get my head around all of these, so any help will be appreciated! 1)the number of goals scored during a football match 2)the height in inches of an individual 3)the number of...

I have been doing some questions on Binomial Series expansion and have been stuck on this particular question for a long time and desperately need some guidance. Q) Expand (1/(sqrt(1-b^2(sin^2)x)))), where b = sin(1/2(theta)) as a binomial series. Here is what I have done so far... Let...