2n12n1 becomes 12n2n1 My question is why do the exclamation

Solution

! - its called factorial.

n! = n(n-1)(n-2)(n-3) ......3.2.1       (upto 1)

so (2n-1)! = (2n-1)(2n-2)(2n-3)(2n-4).....3.2.1

and (2n+1)! = (2n+1)(2n)(2n-1)(2n-2)......3.2.1

so (2n-1)!/(2n+1)! = (2n-1)(2n-2)(2n-3)(2n-4).....3.2.1 / (2n+1)(2n)(2n-1)(2n-2)......3.2.1

lower as everything of upper term but also have extra (2n+1)(2n)

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

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