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:

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