Fundamental Principle

Mathematical induction is a method used to prove that a statement holds true for all natural numbers k.

Let P(n) be a statement defined for each positive integer n.

Then P(n) will be true for all positive integers n if the following two conditions are satisfied:

(1) P(1) is true.

(2) P(k) is true for some integer k + 1 implies that P(k + 1) is true.

Because all the other values can use the result from the (1) and (2),

Therefore, you can conclude that all the conditions with integers n are true.