How do you simplify $(2n!) / (n!)$ ?

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Answer 1 · 2016-07-02T23:05:51

$(2n!) / (n!) = prod_{k=n+1} ^{k=2n}k$

Suppose that we need

$(8!)/(4!) = (1 cdot 2 cdot 3 cdot 4 cdot 5 cdot 6 cdot 7 cdot 8)/(1 cdot 2 cdot 3 cdot 4) = 5 cdot 6 cdot 7 cdot 8$

then

$(2n!) / (n!) = prod_{k=n+1} ^{k=2n}k$

How do you simplify (2n!) / (n!)(2n!) / (n!)?