Step-by-step explanation:
The statement "6n-1 is divisible by 5" is true for all natural numbers n.
Base case: When n=1, 6n-1=6-1=5, which is divisible by 5.
Inductive step: Assume that the statement is true for some natural number k, that is, 6k-1 is divisible by 5. We need to show that the statement is also true for k+1, that is, 6(k+1)-1 is divisible by 5.
6(k+1)-1=6k+6-1=6k+5=5(k+1)+1.
Since 6k-1 is divisible by 5, and 5 is a positive integer, 5(k+1) is also divisible by 5. Therefore, 1 is added to a multiple of 5, which is still a multiple of 5. Hence, 6(k+1)-1 is divisible by 5.
By the principle of mathematical induction, the statement "6n-1 is divisible by 5" is true for all natural numbers n
