Expanding a factorial

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Can you explain me how we got this identity?

$$\frac{1}{(3n)!}$$ the same as $$\frac{(3n)!}{(3n+3)!}$$ I have been trying to expand, but didn't get the same.

Thanks.

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2 Answers

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they are not same , consider $n=1$ , you have $\frac{1}{3!}=\frac{1}{6}$ and on the other hand $\frac{3!}{6!}= \frac{1}{120}$

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If you expand $$(3n+3)!=(3n+3)\times(3n+2)\times(3n+1)\times(3n)!$$ So $$\frac{(3n)!}{(3n+3)!}=\frac 1 {(3n+3)\times(3n+2)\times(3n+1)}$$

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