Question #661df
2 Answers
Explanation:
This expression can't really be simplified algebraically...
With that said, for fun I'll simplify the expression
#((n+1)!)/(n+1)#
In order to simplify the expression
#((n+1)!)/(n+1)#
one thing we could to is set up a table of values by plugging in numbers for
-
#n = 1# : -
#"result" = 1# -
#n = 2# : -
#"result" = 2# -
#n = 3# : -
#"result" = 6# -
#n = 4# : -
#"result" = 24# -
#n = 5# : -
#"result" = 60#
You may be noticing a pattern here: these values yield the same things if the expression were
-
#1! = 1# -
#2! = 2# -
#3! = 6# -
#4! = 24# -
#5! = 60#
Therefore,
#((n+1)!)/(n+1) = color(blue)(n!#
We can also use the definition of the factorial, multiplying values decreasing by
#((n+1)!)/(n+1) = (cancel((n+1))(n)(n-1)(n-2)(n-3)(n-4))/(cancel(n+1))#
Notice how after the two terms are canceled, we're left with
#(n)(n-1)(n-2)(n-3)(n-4)#
Which is equivalent to
#(n)(n-1)(n-2)(n-3)(n-4)... = color(blue)(n!#
It cannot be simplified.
Explanation:
I suspect this question has a typo. If the question was
(note the additional !), then it could be simplified.