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

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