By use of mathematical induction proove that a) [ 3+6+12+...+3 n=(3 n(n+1))/(2) ]

To prove the given statement using mathematical induction, we will follow the standard steps of induction.**Base Case:**Let's start by checking the base case, which is when .Substituting into the given equation, we have: Simplifying the left-hand side, we get: So, the base case holds true.**Inductive Step:**Now, let's assume that the statement is true for some arbitrary positive integer , i.e., we assume that: We need to prove that the statement is true for , i.e., we need to show that: Using the inductive hypothesis, we can rewrite the left-hand side as: Now, let's simplify the right-hand side: Thus, we have shown that the statement holds true for if it holds true for .By the principle of mathematical induction, we can conclude that the given statement is true for all positive integers .