# Too many factorials!

$\large \dfrac{(100!+99!)(99!-98!)(98!+97!)\cdots(2!+1!)}{(100!-99!)(99!+98!)(98!-97!)\cdots(2!-1!)}$

The value of the above fraction can be written as mixed fraction $$a\dfrac{b}{c}$$, where $$b$$ and $$c$$ & $$a$$ and $$b$$ are co-prime, but $$a$$ and $$c$$ are not co-prime. What is the product of $$a$$, $$b$$, and $$c$$?

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