For a fixed positive integer n prove that: ` D = |[n!, (n+1)!, (n+2)!],[(n+1)!,(n+2)!,(n+3)!],[(n+2)!,(n+3)!,(n+4)!]|= ( n !)^3(2n^3+8n^2+10n+4 `)

For a fixed positive integer n , if Delta=|[n !,(n+1)!,(n+2)!],[(n+1)!,(n+2)!,(n+3)!],[(n+2)!,(n+3)!,(n+4)!]| , then show that [Delta/((n !)^3)-4] is divisible by ndot

For a fixed positive integer n if D= |(n!, (n+1)!, (n+2)!),((n+1)!, (n+2)!, (n+3)!),((n+2)!, (n+3)!, (n+4)!)| = the show that D/((n!)^3)-4 is divisible by n.

For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)!(n+2)!(n+3)!(n+4)!| , then show that [/((n !)^3)-4] is divisible by ndot

For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)!(n+2)!(n+3)!(n+4)!| , then show that [/((n !)^3)-4] is divisible by ndot

For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)!(n+2)!(n+3)!(n+4)!| , then show that [/((n !)^3)-4] is divisible by ndot

For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)!(n+2)!(n+3)!(n+4)!| , then show that [/((n !)^3)-4] is divisible by ndot

If n ge 1 is a positive integer, then prove that 3^(n) ge 2^(n) + n . 6^((n - 1)/(2))