Thread: factorial long division (or not?)

my textbook shows the result of n!/(n!+1) to be

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

also latex is throwing errors whenever i use factorials.

It's actually n!/(n + 1)! = 1/(n + 1). This is because (n + 1)! = (n + 1)n!.

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

It's because N! = N(N - 1)(N - 2)...(3)(2)(1) = N(N - 1)!.

What happens if N = n+1?

should be N!= n+1(n)(n-1)(n-2)...(4)(3)(2)(1)=N+1(N)!

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!

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, , is not true if .

It is true that

Originally Posted by Plato

What you posted, , is not true if .

It is true that

my math textbook is absurd, it does not mention that this relation is only true in a single scenario.

Originally Posted by skyd171

my math textbook is absurd, it does not mention that this relation is only true in a single scenario.

I am not sure how to read that.
But the is true: