<PRE><B>Question 89892</B>
6+12+18+....6n=3n(n+1) 

Proof by induction

 True for n = 1

 6 = 3(1)(1+1)

 Assume true for n = k

 6+12+18+....6k=3k(k+1)


  Then show that 

 6+12+18+....6(k+1)= 3(k+1)(k+1+1)

  We add 6(k+1) to both sides of

 6+12+18+....6k=3k(k+1)

 6+12+18+....6k +6(k+1) =3k(k+1) + 6(k+1)

                        = 3(k+1)(k + 2)

                        = 3(k+1)(k+1+1)

  So true for n = k+1

 Since true for n=1 it is true for n=2,3,... 

 Thus true for all natural numbers n by mathematical induction


  
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