Question

-4n(-2n-3)-2n(1+2n) = ? find value of n​

Answer 1

Answer:

Let SA=(2n+1)(2n+3)(2n+5)⋅(4n−1)

Let SB=(2n+1)(2n+2)(2n+3)(2n+4)(2n+5)(2n+6)…(4n−1)(4n)

⟹SB=(4n)!(2n)!(E01)

⟹SB=(2n+1)(2n+3)(2n+5)⋯(4n−1)=SA(2n+2)(2n+4)(2n+6)⋯(4n)

⟹SB=SA⋅2(n+1)⋅2(n+2)⋅2(n+3)⋯2(2n)

⟹SB=SA⋅2n⋅(n+1)(n+2)(n+3)⋯(2n)

⟹SB=SA⋅2n⋅(2n)!n!=(4n)!(2n)![ From (E01)]

⟹SA=[(4n)!(2n)!]÷[2n⋅(2n)!n!]=(4n)!⋅n!2n⋅(2n)!⋅(2n)!

⟹SA=(4n2n)⋅n!2n