Prove by PMI
n(n+1)(n+5) is divisible by 6 for all n belongs to natural numbers
Assume P(k) is true:
K(k+1)(k+5)=6m [multiple of 6]
Consider P(k+1)=( k+1) (k+2)( k+6)
=k(k+1)(k+2)+6(k+1)(k+2)………split (k+6)
=6n+6(….)…………………………………………….k(k+1)(k+2) product of 3 consecutive no’s is
divisible by 6
therefore it is true for all natural nos