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I know "!" means e.g. 5!=5x4x3x2x1 but how about [3(n+1)!]/[5n!]?

Can you see how n! = n(n-1)!?

or that (n+1)! = (n+1)n! ?
just like 8! = 8(7!)

then [3(n+1)!]/[5n!]
=3(n+1)n! / 5n!
=3(n+1)/5

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