Answer:
Step-by-step explanation:
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
