# factorial long division (or not?)

• Apr 21st 2011, 08:11 AM
skyd171
factorial long division (or not?)
my textbook shows the result of n!/(n!+1) to be $\displaystyle \frac{1}{n+1}$

Does anyone know how they arrive at this result? Even wolfram shows something different.

also latex is throwing errors whenever i use factorials.
• Apr 21st 2011, 08:13 AM
Prove It
It's actually n!/(n + 1)! = 1/(n + 1). This is because (n + 1)! = (n + 1)n!.
• Apr 21st 2011, 08:21 AM
skyd171
Thanks. why is it equal to that? is this a rule for distributing factorials over parentheses? i have not seen that rule before.
• Apr 21st 2011, 08:22 AM
Prove It
It's because N! = N(N - 1)(N - 2)...(3)(2)(1) = N(N - 1)!.

What happens if N = n+1?
• Apr 21st 2011, 08:28 AM
skyd171
should be N!= n+1(n)(n-1)(n-2)...(4)(3)(2)(1)=N+1(N)!
• Apr 21st 2011, 08:32 AM
Prove It
First of all, you MUST use brackets where they are necessary and second, N and n are different.

It should be N! = (n + 1)(n)(n - 1)...(3)(2)(1) = (n + 1)n!.

Therefore (n + 1)! = (n + 1)n!
• Apr 21st 2011, 08:32 AM
Plato
Quote:

Originally Posted by skyd171
Thanks. why is it equal to that? is this a rule for distributing factorials over parentheses? i have not seen that rule before.

What you posted, http://quicklatex.com/cache3/ql_7484...4e9e03f_l3.png, is not true if $\displaystyle n\ne 1$.

It is true that
• Apr 21st 2011, 09:13 AM
skyd171
Quote:

Originally Posted by Plato
What you posted, http://quicklatex.com/cache3/ql_7484...4e9e03f_l3.png, is not true if $\displaystyle n\ne 1$.

It is true that