Answer
See explanations.
Work Step by Step
Step 1. Prove that the statement is true for $n=1$: $7^1-1=6$ is divisible by 6, thus it is true for $n=1$
Step 2. Assume the statement is true for $n=k$: we have $7^k-1=6m$ is divisible by 6, where m is an integer.
Step 3. Prove that it is also true for $n=k+1$:
$7^{k+1}-1=7\times7^k-1=7(6m+1)-1=42m+6=6(7m+1)$ is also divisible by 6.
Thus, the statement is also true for $n=k+1$
Step 4. With mathematical induction, we have proved that the statement is true for all natural numbers n.
