Factorial Definition and 162 Threads

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.

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...

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...

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