Question

Prove that:(2n)!/n! = { 1*3*5....(2n-1)} 2ⁿ

Answer 1

LHS = (2n)!=(2n)(2n−1)(2n−2)(2n−3)............4 . 3 . 2 . 1=[(2n). (2n−2)...........4 . 2] × [(2n−1)(2n−3)...........3 . 1]=2n[n(n−1)(n−2)......2.1] × [(2n−1)(2n−3)...........3 . 1]=2n . n! × [1.3.5.........(2n−3)(2n−1)]=RHS
or it can be written as you asked in the question if we bring n! to left