How do you simplify the factorial expression #((n+2)!)/(n!)#?
1 Answer
Feb 8, 2017
# ((n+2)!)/(n!) = (n+2)(n+1)#
Explanation:
Remember that:
# n! =n(n-1)(n-2)...1 #
And so
# (n+2)! =(n+2)(n+1)(n)(n-1) ... 1#
# \ \ \ \ \ \ \ \ \ \ \ \ \ \=(n+2)(n+1)n!#
So we can write:
# ((n+2)!)/(n!) = ((n+2)(n+1)n!)/(n!) #
# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =(n+2)(n+1)#
