Proving the correctness of iteration and recursion

Basically, iteration and recursion are both loops. The difference is that recursion continues to call the function itself until it gets to a base case, while iteration has variables which change after each iteration.
Considering proofs of the correctness of iteration or recursion , I find out that it is easier to prove recursion by using complete induction. I assume P(1) and P(2) and ... and P(n-1) is true where n is a parameter about the function. Then I check that when the function calls itself, the parameter about the just called function is within the domain of (1, n-1) so that by assumption, the just called function returns the correct result.
As far as iteration is concerned, I need to have loop invariants which are true after each iteration. Loop invariants depends on the i-th iteration (i = 0, 1, 2,...), so the expression for loop invariants has parameter i. I need to prove the expression holds for every i using simple induction. Also, it's necessary to prove the iteration terminates. To prove that, I need to find an expression composed of loop invariants and prove it is a decreasing sequence so that the iteration terminates at last.