Question

Prove by the principle of mathemaatical induction3.6 + 6.9 + 9.12+.....+ 3n (3n + 3) = 3n(n + 1)(n + 2)

Answer 1

3.6 + 6.9 + 9.12 + 3n *(3n+3)  = 3n (n+1)(n+2)

1)  let n = 1
      then    3. 6 =  3*1 (1+1) (1+2) = 18      correct.
2)  let the given expression be true for n = k.
     Then  for  n = k+1,
  3.6 + 6.9+9.12+....+ 3k (3k+3) + (3k+1) (3k+4)
   =  3 k(k+1)(k+2) + (3k+3)(3k+6)
  =   3( k+1) (k+2) [ k + 3]
  This is in the form of  3 n (n+1)(n+2)

So that is proved by Induction.