I need help to solve this question :
Use induction to prove that, for n>=0:
3*5^0 + 3*5^1 + 3*5^2 + 3*5^3 + ...+ 3*5^n = 3*(5^(n+1)-1)/4
As 3 is a common factor on both sides it is sufficient to prove:
To start we need to prove that base case (where )
Then assume it true for , then show that:
implies that:
You do this by adding to both sides of the assumed case, that is:
and show that the right hand side is equal to
CB