Question #de96e

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Answer 1 · 2017-12-10T03:08:41

Remember the definition of a factorial, and find where the denominator is a factor of the numerator. #= ((n+1)(n))/2#

It will be assumed that the problem is intended to read:

#((n+1)!)/((n-1)!2!#

Recall that #(n+1)! = (n+1)(n)(n-1)(n-2)...(1)#

Recall further that #(n-1)! = (n-1)(n-2)(n-3)...(1)#

Knowing that we can rewrite this:

#= ((n+1)(n)(n-1)!)/((n-1)!2!)#

#(n-1)!# cancels on top and bottom, giving:

#= ((n+1)(n))/(2!)#

2 factorial is simply 2 #(2! = 2*1)#

Thus this gives us:

#= ((n+1)(n))/2#