Factorial Definition and 159 Threads

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

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.

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...

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...

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...

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

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...

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

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