Factorial Definition and 162 Threads

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...

In the situation where differences between consecutive squares, (or consecutive cubes, consecutive x^4, etc.) are calculated, then the differences between those differences are calculated, and then the differences of those differences, and so on until you reach a constant number at a deep...

Homework Statement This is not a homework problem. I was just wondering the logic and intuition behind the "formula" for finding the number of zeros given the factorial of a number. Homework Equations Formula : round(n/5) + round(n/25) + round(n/125)+...+round(n/5^n) Here, round...

Factorial of 0=1 ?! Can anyone please explain to me the proof that the factorial of 0 is 1?

First of all apologize for my english, I'm french and I'll do my best to be understandable. So my question is about factorials. how do you manage to say that (n+1)!=(n+1)n! ? I tried to develop this but my brain is just not able to understand how I'm suppose to do. Could someone please show...

Homework Statement \sum(n-1)!/(n+2)! 2. The attempt at a solution I tried the ratio test and came up with the lim_{}n\rightarrow\infty n/(n+3) = 1 which gives no information on convergence or divergence. I'm trying to find absolute or conditional convergence so what else can I do?

Id like to know some basic representations of factorials n!, (n+1)!,(n-1)! ext..

Homework Statement Classify the series as absolute convergent, conditionally convergent, or divergent. \Sigma^{\infty}_{k = 1} (-1)^{k-1}\frac{k!}{(2k-1)!} Homework Equations The Alternating Series Test: conditions for convergence decreasing lim --> infinity ak = 0 The...

Hello everyone! Homework Statement n!/(n-r)! = n(n-1)(n-2)...(n-r+1) where r is the number of objects we want from n distinct objects (3 billiard balls out of 16) I don't understand what the last term in the expansion means, the (n-r+1). For example, suppose we have 5 distinct...

So I've been asked to prove that: lim (n-->infinity) [2^n]/sqrt(n!) = 0 I've tried fiddling with Stirling and L'Hospital, but can't find my way through it. Any thoughts?

Hi, I want to find the derivative of factorial function f(x)=x! and i found this integral, f(x)=x!=\int_{0}^{\infty}e^{-t}t^xdt when i take derivative of this \frac{d}{dx}f(x)=\frac{d}{dx}\int_{0}^{\infty}e^{-t}t^xdt=\int_{0}^{\infty}e^{-t}t^xlnxdx How do i find this integral? Please...

Homework Statement Determine whether the series below is convergent or not: \sum 7*\frac{n!}{n^{n-10}} n=8 and the series goes to infinity (Sorry, I couldn't get the formatting correct.) Homework Equations n/aThe Attempt at a Solution Well, originally I thought the series was divergent...

If we define an addictive factorial for any integer n: f(n) = n + (n-1) + (n-2) ... 0 1!+ = 1 2!+ = 2+1 = 3 3!+ = 3+2+1 = 6 4!+ = 4+3+2+1 = 10 5!+ = 15 is it possible to extend it to real or possibly complex numbers by analytic continuation? just like the gamma function extends the factorial.

Can somebody demonstrate : \[ \frac{n}{{\sqrt[n]{{n!}}}} < \left( {1 + \frac{1}{n}} \right)^n \] ITS not A HOMEWORK

Can somebody please explain to me this simplification and how it's done? \frac{n!}{(2n)!} = \frac{1}{(2n)(2n-1)...(n+1)} Thanks a lot.

Homework Statement Determine the divergence or the convergence of the sequence. If it converges find its limit. a_{n} = (\frac{(n)!}{2n!+1}) The Attempt at a Solution All I know about factorials is for example 4! = 1*2*3*4. So as far as limits go I'm clueless. please help!

Homework Statement I am solving for t using this equation: d = !(v + 0)t; My d=.984 and v=1.9 I don't know what to do with the "!" Homework Equations d = !(v + 0)t; The Attempt at a Solution In a problem with different numbers I was able to solve for t by dividing and...

Hi I am relatively new to C++ and I am having a little trouble understanding, in detail, the logic of this recursive function. Can someone tell me if my reasoning this out is correct? int fact (int n) { if (n==1) return 1; else return (n*fact(n-1)); } So if the...

i m unable 2 get the output for the followin c program. The factorial program is correct i think there is problem in the FOR loop..guess its goin infinite...pls help #include<stdio.h> #include<math.h> factorial(int); main() { int n,count,i; float number,x,series; printf("nter number...

Homework Statement P(n, 4) = 40[P(n-1, 2)] Homework Equations ? The Attempt at a Solution I boiled this down to the equation n!/(n-4)! = 40[(n-1)!/(n-3)!]. The problem is, I have no idea how to perform the correct operations on these factorials. I found the answer to be n = 8...

Homework Statement \frac{(kn)!}{(kn+k)!} I was thinking: (kn)! = 1*2*3...(kn) (kn+k)! = 1*2*3...(kn)(kn+k) and I would be left with 1/kn+k But my book has the answer as: \frac{1}{(kn+k)(kn+k-1)...(kn+1)} How can I arrive to that?

Homework Statement I'm trying to prove k*(k!)=(k+1)!-1 Homework Equations The Attempt at a Solution This is how far I've gotten: k[k(k-1)(k-2)...1)]

Why does Mathematica sometimes give Gamma, the funtion and sometimes !, the factorial? What is the differences?

Substitute each of the letters by a different decimal digit from 0 to 9 to satisfy this cryptarithmetic equation: (ABCD)*(EFEGBH) = (EC)! Note: None of A and E can be zero.

Why is the first part of this inequality true? 1/(n+1)! [ (1 +1/(n+1) +1/(n+1)^{2} +...+ 1/(n+1)^{k} ] < 1/(n!n) < 1/n

Homework Statement lim n -> infinity for (n!)^(1/n) Homework Equations The Attempt at a Solution hmm, i know that lim n approaches infinity, (n)^(1/n) will go to 1, but issit the same for n!?

I don't have much experience in this, and hopefully someone can recommend the right type of book that I need to look thru in order to solve future problems like this. I have to have a formula for the nth derivative. I have like in the numerator, but Idk how to express it properly. 5 5 x 10...

Please can anybody help me find this limit?

Homework Statement I was just wondering if n!=n(n-1)! is completely general. Does it hold even for non-integer n? Homework Equations The Attempt at a Solution

For the factorial (2n+1)!, I thought the previous term is going to be (2(n-1)+1), which is equal to (2n-1). Thus (2n+1)!= (2n+1)(2n-1)! However, in the textbook, they have it as . a_n= \frac{(2n-1)!}{(2n+1)!}=\frac{(2n-1)!}{(2n+1)(2n)(2n-1)!} Are they wrong or I am wrong? Thanks!

I was looking at the web page containing a derivation for the Poisson distribution: http://en.wikipedia.org/wiki/Poisson_distribution which derives it as the limiting case of the binomial distribution. There is a simplification step which I am missing, which is the step(s) between...

[SOLVED] Factorial Limits Homework Statement lim n^n x->00 n! Homework Equations Instructor said to use the Squeeze theorem. The Attempt at a Solution So far I have not been able to come up with much. I have looked at breaking the top apart into (n)(n)(n)...(n) and the bottom into...

Homework Statement My task is to determine whether the following series is convergent or not. \sum_{n=1}^{\infty}\left(\frac{n}{e}\right)^{n}\frac{1}{n!} The Attempt at a Solution The limit of the terms is zero, so the series might be convergent. I tried the ratio test, but the...

Hello all! In solving some math problems, I encountered the following sum: \sum_{k=1}^{r+1} kb \frac{r!}{(r-k+1)!} \frac{(b+r-k)!}{(b+r)!}. \quad \mbox{(eqn.1)} Now, I have asked Maple to calculate the above sum for me, and the answer takes a very simple form: \frac{b+r+1}{b+1}. \quad...

I'm working on the limit of the sequence (Xn) = (n!)^(1/n) Pretty sure it diverges as n goes to infinity, but unsure how to show it. Any hint would ge greatly appreciated.

Is there such a thing? The factorial is usually defined as n! = \prod_{k=1}^n k if k is a natural number greater than or equal to 1. Is there an operation that is defined as \sum_{k=0}^n k if one wants to find, for instance, something like 5+4+3+2+1? I ask because I was thinking about...

Homework Statement Why does the limit as n -> infinity of [3^(n+1)]/(n+1)!] * n!/(3^n) equal the limit as n -> infinity of 3/(n+1)? Homework Equations The Attempt at a Solution I have never encountered this before.

Homework Statement (2n-1)!/(2n+1)! Homework Equations The Attempt at a Solution ...2n-2*2n-1 ------------ (pretend that's a divider) ...2n-2*2n-1*2n*2n+1 Is the answer 1/[2n*2n+1]?

Hi, I have a question about factorials that I'm hoping someone can help me with. I know that the factorial n! means the product of the integers from 1 to n, for example if I have 4! then this is equal to 4 x 3 x 2 x 1 = 24, but I have an equation which contains the term: k(n-1)! I am...

Hello. Do anyone know the shortcut or trick of taking factorial directly? for example : 9! = 9*8*7*6*5*4*3*2*1. it is very time consuming method to multiply all these terms to get answer. please tell me easy mathod. thank you

Just wondering: Why does 0!=1 ? Thanks

#include<qvalidator.h> //int input; void Factor::init(){ InputEdit->setValidator(new QDoubleValidator(InputEdit)); FactorNumber(); InputEdit->selectAll(); } int Factor::factorials(int n){ if(n<=1) return 1...

Hey, I was wondering if someone could help me with a specific type of question that I can't seem to understand without an answer key. Anyway, it's rewriting expressions with factorial notation so that they no longer have factorial symbols. Example: Simplify without using the factorial...

I don't understand this conversion! \sum_{n=1}^\infty \frac{sin(n\pi /2)}{n!} = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} I know that the numerator of the left side is 0 when n is an even number. When n is odd, the numerator is either +1 or -1. But how do i continue?

Any ideas on how to prove this? (n+\tfrac{1}{2})! = \sqrt{\pi} \prod_{k=0}^{n}\frac{2k+1}{2}

how many consecutive zeros are at the end of 52! ?

Why is zero factorial equal to 1?

how can i find the number of zeroes at the end of 100! how can i find the number of zeroes at the end of n! thanks in advance.