What is Factorial: Definition and 162 Discussions

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n:

For example,

The value of 0! is 1, according to the convention for an empty product.The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there are n!.
The factorial function can also be extended to non-integer arguments while retaining its most important properties by defining x! = Γ(x + 1), where Γ is the gamma function; this is undefined when x is a negative integer.

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  1. A

    Find zeros at the end of a factorial

    I found the following problem online, and can't seem to start it. How many zeroes are at the end of 4^{5^6}+6^{5^4}? I know how to find zeros at the end of a factorial, but I can't do it with powers. Any suggestions? Thanks.
  2. M

    Factorial Sequences: Real Life Examples

    Hey there everyone, We were discussing factorial sequences in my last pre-calculus class. Factorials are pretty cool. I asked if they had any rel world applications or examples I could put into my notes. She then told us if we could find an example that we'd get extra credit on our quiz, I'm...
  3. T

    Series and Factorial: Solve the Sum of Infinite Terms

    I’ve been playing around with the infinite series: \sum_{k=1}^\infty \frac{k}{(k+1)!} I haven’t really gotten anywhere with it however I punched it into my calculator and it determined the sum to be 1. And the sum of n terms of the series equals 1-\frac{1}{(n+1)(n!)} Why is this so...
  4. S

    Question about sum of integer involving factorial notation

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

    Evaluating 12 C 2: How to Simplify Without a Calculator

    Ok just a basic question. We are given 12 C 2 to evaluate. Which equals 12! / (10!2!) Is there an easier way to simplify it. We are asked to do it without a calculator. Thanks.
  6. C

    Factorial in example problem, I'm confused

    I'm confused from one step to the next in the book. In the first step, they have (n+1)! then in the next step the write that as (n+1)n! so (n+1)! = (n+1)n! ? I don't understand that, can someone explain it to me ? ( I am very unfamiliar with factorials, this is like some...
  7. maverick280857

    Square of n factorial is greater than n to the power n

    Hi I need some help figuring out how to do this problem: Prove that for every natural number n, (n!)^{2} > n^n By rewriting this as (n!)^{\frac{1}{n}} > \sqrt{n} I can see that I have to prove that given a sequence of natural numbers {1, 2, 3, ..., n}, the geometric mean of n numbers...
  8. R

    Exploring the Prime Factorial Conjecture

    Here is a tentative conjecture that needs to be tested. [P! + P]/P^2 = INTEGER if and only if P is a prime number P! is P factorial, e.g. 3*2*1 , 5*4*3*2*1 , 7*6*5*4*3*2*1, etc...
  9. E

    Is There a Simple Way to Compute Derivatives for Factorials Beyond the Basics?

    Is there a simple neat process to compute derivates for factorials beyond the simple ones...
  10. MathematicalPhysicist

    An integral and a deravative of a simple factorial

    how can you find the integral and the derevative of a simple factorial f(x)=x! (to find what f'(x) equals and what Sf(x)dx equals)? as i see it you have progressive multiplications, f(x)=x(x-1)(x-2)...*(x-k), which is the product of x-k where k=0 till infinity, should i take logarithms on both...
  11. M

    How can I write this sequence in terms of factorials?

    Can anybody help me solving this? Write in terms of factorials n((n^2)-1) The correct answer is (n+1)!/(n-2)! but I don't know how to get there, and since it's week- end I have no chance to ask anyone teachers, etc. //Martin
  12. O

    How to perform factorial operation

    I don't know if this is the right place for this question, but here it goes. Could someone explain how I would go about solving for x of x=(5/6)! Thanks
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