Factorial Definition and 159 Threads

(A) Total no. of integer ordered pairs $(x,y)$ in $x^2-y! = 2001$ (B) Total no. of integer ordered pairs $(x,y)$ in $x^2-y! = 2013$ My Trail :: (A) Given $x^2-y! = 2001 = 3 \times 23 \times 29 \Rightarrow x^2 -y! = \left(3\times 23 \times 29\right)$ means $(x^2-y!)$ must be divisible by...

Find the exact value of the series $$\frac{1}{4!}+\frac{4!}{8!}+\frac{8!}{12!}+\frac{12!}{16!}+\cdots\cdots$$

Homework Statement $$\lim_{n \to \infty}\frac{10^n}{n!}$$Homework Equations Do I need to use something as advanced as Stirling approximation? This question appears in page 5 of Boas Mathematical Methods, there's no prior discussion on factorial or convergence test and etc. The Attempt at a...

Homework Statement These trickly little buggers always seem to confuse me. I need to find out whether or not the sequence is increasing, decreasing or neither. An=(n!)2/(2n)! Homework Equations The Attempt at a Solution I'm pretty sure that it's a decreasing sequences but when I expand and...

Hi members, gamma (n+1)=n! Now I have the following: gamma(2(n+3/2))=gamma(2n+1) What is factorial notation for this?? Thank you

Homework Statement Hi everyone! Me and my colleague are working our way through Harold J Larson's "Introduction to Probability Theory and Statistical Inference: Third Edition", and we found something interesting. We both have the same edition of the text, but mine is slightly newer?, and...

Homework Statement To write a C++ program to find the factorial of the number input 'a'. Homework Equations the factorial evaluated is denoted as 'f' i is the counter The Attempt at a Solution Pls check if my program is correct...(here f is the value of factorial and a is the...

Why is it that (x + y)!=(x + y)(x + y - 1)(x + y - 2)...(x + 1)x! Where did the last "x!" come from? Thanks

Homework Statement Show that the folowing holds: \lim_{n\to\infty} \frac{(n!)^2 4^n}{(2n)!} = \inftyHomework Equations It can be shown that \frac{(n!)^2 4^n}{(2n)!} = \prod_{k=1}^n \frac{4k}{k+n}The Attempt at a Solution If I can proove that \lim_{n\to\infty} \ln\left[\frac{(n!)^2...

I was studying about infinite products that I got to the relation below in http://mathworld.wolfram.com/InfiniteProduct.html \infty != \sqrt{2 \pi} It really surprised me so I tried to find a proof but couldn't. I tried to take the limit of n! but it was infinity.Also the limit of...

Homework Statement find z transform of: x[n] = (1 / n!) *u[n] u[n] is the unit step Homework Equations z transform equationX(z) = Ʃ x[n] * z-n summation is from -∞ to +∞ The Attempt at a Solutioncancel the u[n] by changing the bounds of the summation now it is from 0 to +∞It's at this...

I need to simplify this expression and I don't know how to deal with the factorials in the sum e^{-(\lambda + \mu)}\sum_{k=0}^w \frac{\lambda^k \mu^{(w-k)}}{k!(w-k)!} Can anybody give me a hint on how to sum over the factorials?

I was searching for derivative of factorial. Many say that gamma function is the derivative of the factorial. Is that true because I searched about gamma function and it doesn't say anything like that. Thanks a lot

Homework Statement The sequence is [SIZE="3"]a_n = \frac{n^P}{e^n} Homework Equations The Attempt at a Solution If I did L'Hopital's rule P times, would the final product look like: [SIZE="3"]P!\times lim_{n \rightarrow \infty} = \frac{1}{e^n} ?

Is it possible to find the factorial of a negative real number ? If possible, then what is its practical application ?

Homework Statement [SIZE="3"]a_n = \frac{(2n -1)!}{(2n)^n} Homework Equations The Attempt at a Solution I am not exactly sure how to solve this problem.

The sum of "(n+3)!/(3n+2)!" with n=1 to n=inf. How do I find if it converges or diverges by using one of the tests(ratio, roots series, divergence, etc)?

Homework Statement Factor x + 5+ 6x^-1 Factor x^(3/2) + 2x^(1/2) - 8x^(-1/2) Homework Equations None given. The Attempt at a Solution I have tried factoring normally, it's just not working out though (for either part of the question.) I've never had to deal with this in a math...

I saw this in my book and I'm having a difficult time figuring out how this formula was manipulated algebraically to equal the other side. I know that it works because I've used it several times but I can't show that it is true. \frac{n(n-1)...(n-r+1)}{r!} = \frac {n!}{(n-r)!r!} One of...

\frac{2 i}{(2 i + 1)!} = \frac{1}{(2 i)!} - \frac{1}{(2 i + 1)!} Could anybody please show what it is that needs to be done on LHS to get to RHS in this identity.

Homework Statement Find all positive integer solutions for a, b and c to the equation: a!b! = a! + b! + c!Homework Equations n! = n(n-1)(n-2)... The Attempt at a Solution I'm not having much progress with this. I've tried rewriting it as (a! - 1)(b! - 1) = c! + 1 and I've found one...

maybe its simple permutation and combination technique... I ve tried to resolve it on my own but I couldn't...The textbook which I read simply mentions it to be obvious..can anyone please elucidate me the logic behind factorials of "independent components of tensor curl" and levi cita Can...

How to state null and alternative hypothesis for 2k factorial design of two factors? The Attempt at a Solution All i can think of right now is null hypothesis - Factor A effects not significant. alternative hypothesis - Factor A effects significant null hypothesis - Factor B effects...

Ʃ \frac{(4n)!}{n!(2n)!} I tried the ratio test, but if my solution has a limit which goes to infinity. Hence the test is inconclusive. (Or does L->inf imply divergence as L>1 ?) Any ideas what other test might be useful ? PS: I have used the idea that (2(n+1))! = (2n+2)! = (2n+2)(2n+1)(2n)...

if I have n slots [1,2,3,4,5,...n] where I must use numbers from 1 through n, and I have to ensure that none of them were reused... the way I figure to make sure that none of the numbers are reused is to multiply the values in each slot and compare them against n! e.g. [1,2,3,4,5] would be...

Homework Statement \frac{1^2*3^2*5^2...(2n-1)^2}{2^2*4^2*6^2...(2n)^2}<\frac{1}{2n+1} Edit: Must be proven without using induction. Homework Equations The Attempt at a Solution I understand the LHS is the same thing as \frac{(2n-1)!}{(2n)!} And (2n)! = k!2^k & (2n-1)! =...

Homework Statement Determine if the sequence {an} below converges or diverges. Find the limit of each convergent sequence an = n!/nn Hint: Compare with 1/n . Find the limit of the sequence {an} if it converges. I missed the lesson on factorials, and the book is useless. Sorry...

Dear Fellows, I want to write rational numbers factorial in my MATLAB program for integers factorial command is factorial(n) but for rational numbers such as 0.1 or 0.2 this command is not working can anyone guide me to solve this issue ? Regards

Hi all, I know what factorials are, obviously, and permutations and combinations, but what I Don't know is, given a problem with factorials in it, is there a general format for solving? For instance, an old AMC 10 problem: 10B-#11. What is the tens digit in the sum 7! + 8! + 9! + . . . +...

Homework Statement Show that n/(n+1)!=(1/n)-(1/(n+1)!) I am totally lost on the algebraic steps taken to come to this conclusion. It is for an Infinite series. Thanks

Hello, I've been working on solving the equation y''-2xy'+2py=0. where p is a positive integer. I've assumed y=\sum a_{n}x^{n} for n=0 to inf I'm getting two formulas for a_{n} One is for odd n, the other for even n, related to a_{0} and a_{1} However, the relation involves something that...

Homework Statement In my calculus book they have the following simplification: \frac{k!}{(k+1)!} = \frac{1}{k+1} I do not quite understand how that's occured.

How to prove (2n)!=2^nn! for example (2)!=2^11!=2 (4)!=2^22!=8 ... (2n)!=2n(2n-2)(2n-4)...=2^3n(n-1)(n-2)... I see that by intiution but I don't know how to write prove.

Homework Statement Express \frac{1}{(2n+1)!} as the following \frac{(-2)^{n}n!x^{2n+1}}{(2n+1)!} where 0 <= n <= infinity Homework Equations The double factorial for odd integers is (2n+1)! = (2n+1)(2n-1)(2n-3)...1 where 0 <= n <= infinity The Attempt at a Solution...

Homework Statement Write a C++ code factorial.cc that calculates the factorial of an integer by direct multiplication. Start with your code in exercise (3), and modify it so that it gets "n" from the user and prints out n! = 1*2*3*...*(n-1)*n. To do this, use a "for" loop: int nfac...

Homework Statement \sum_{n=0}^{100} 1/n!(100-n)! The Attempt at a Solution Other then obvious attempts to make sense of the equation's incremental and decrements divisor, I can't figure out where to start with this question. Some assistance would be greatly appreciated.

Homework Statement The Attempt at a Solution I have no idea where to start from. I know that e = 1/0! + 1/1! + 1/2! + 1/3! + ... + 1/n! + ... and tried to separate the factorial off the geometric series but had no success.

Homework Statement I need to evaluate the following limit: lim_{n\rightarrow\infty}\left(\frac{1}{n!}\right)^{\frac{1}{3n}} Now, I think I have solved it, but my methods are not rigorous. I am looking to see if my assumptions are sound and if there is an easier way to solve this limit...

Homework Statement I've got to show \sum_{n=0}^{\infty} \frac{(a)_n(-1)_n}{(c)_n n!} = \frac{c-a}{c} where \displaystyle (a)_n = \frac{\Gamma(a+n)}{\Gamma(a)} = a(a+1)...(a+n-1) is the shifted factorial (Pochhammer symbol). The Attempt at a Solution I've been informed that (-1)_n =...

Hi, we know that for all interger m, n_1!\cdots n_k! divides m! where n_1+\cdots+n_k=m. Now I want to show that m! (n!)^m divides (mn)!. We see that (n!)^m divides (mn)! since \overbrace{n+\cdots+n}^{m-terms}=mn Also m!(nm-m)! divides (mn)! similarly. But how could I show my required...

Homework Statement Determine whether 1/n! diverges or converges. So far, we have only learned the comparison tests, p-series, geometric series, divergence test, and integral test, so I can only use these tests to prove it. Homework Equations N/a The Attempt at a Solution I...

so, 6! = 6*5*4*3*2*1 (n+2)! = (n+2)(n+1)(n)! (2n+2)! = (2n+2)(2n+1)(2n)! (500n+3)! = (500n+3)(500n+2)(500n+1)(500n)! Are all these statements correct?

I know that n!=(1)(2)(3)...(n-1)(n) I am confused how I can figure out what (n+2)! is in order to divide it by n! How can I figure (n+2)! out and what is it, so that I won't have to ask if what I got is right. Thanks!

Hi, I've been trying to make another expression for, m \sum(k!) = f(m) k=0 I did one expression that is, f(m) = 2(3(4(5...((m-1)(m+1)+1)...+1)+1)+1)+1 For instance, f(4) = 2(3(4+1)+1)+1 Can you hint me on finding a finite expression for the above expression? Thanks for help.

I know how to expand a factorial of the form (n-2)!. How would one expand (n-n')! ? Would it just be (n-n')? thanks in advance

Is there a method to solve an unknown factorial algebraically? Homework Statement 5040 = a! I found the solution a = 7 through trial and error, was just wondering if a more elegant method exists.

Homework Statement Hello. This is the gist of the question: I have 0 < k < n and I need a formula to show the number of sets of exactly k integers, each chosen from 1, ... , n. Homework Equations n! is the number of distinct ways to rearrange n objects into n slots. The...

Homework Statement N is divisible by 4. N! has exactly 50 zeros. Find N. Homework Equations In case anyone younger doesn't know, Y!=Yx(Y-1)x(Y-2)x(Y-3)x...x3x2x1 The Attempt at a Solution No idea.

Prove or disprove: If n is an integer and n > 2, then there exists a prime p such that n < p < n!.

Why is the equation (A) n!/(n-k)! = n(n-1)(n-2)...(n-k+1) true? For example, let n=4 and k=2, then 4!/2! = 4x3x2x1 / 2x1 = 4x3 = 12. I understand this example, but I can't make the connection with this and the right-hand-side of equation (A). For example, why is our...