Write the expression without using the factorial symbol.
(n+1)!/(n-1)!
my work:
(n+1)!/((n+1)(n-1)!)
=1/(n-1)?
Thanks in advance.
close
(n+1)!/(n-1)!
= (n+1)(n)(n-1)!/((n+1)(n-1)!
= n
hmm..the answer key says its n(n+1), maybe the answer key is wrong
wait, nevermind, I got it :)
thanks :P
You know what?
I looked at "my work" and assumed that was the starting question.
so here it goes once more
(n+1)!/(n-1)!
= (n+1)(n)(n-1)!/n-1)!
= n(n+1)
sorry
I should be more careful when reading questions.
To write the expression (n+1)!/(n-1)! without using the factorial symbol, you can expand both factorials and simplify the expression.
Let's start by expanding (n+1)! and (n-1)!.
(n+1)! = (n+1)(n)(n-1)(n-2)...(2)(1)
(n-1)! = (n-1)(n-2)(n-3)...(2)(1)
Now substitute these expansions into the expression:
(n+1)!/(n-1)! = ((n+1)(n)(n-1)(n-2)...(2)(1))/((n-1)(n-2)(n-3)...(2)(1))
Next, cancel out the common factors in the numerator and denominator:
= (n+1)(n)/(n-1)
So, the expression (n+1)!/(n-1)! can be written as (n+1)(n)/(n-1).
Please note that "1/(n-1)" is not the correct result for (n+1)!/(n-1)! after expanding the factorials.