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.
Q Prove the following for all positive n:
A For n = 1,
The statement is true for n = 1.
For n = k + 1, Assume the statement is true for some integer k >= 1.
The statement is true for n = k + 1. By the principle of mathematical induction, the statement is true for all positive integers n.