Question

how to prove by mathematical induction that (7^n -1) is divisible by 6 for all n=positive integer

Answer 1

hello grace?

Answer 2

Have you done the base case yet?

Answer 3

I don't actually know what the base case is? Is it the series? I tried to do that but I wasn't sure if I had the expression right.

Answer 4

It wants you to show it is true for all positive integers
the first positive integer is 1
so you have to show 6 divides (7^n-1) for n=1

Then after that you have to prove:
\[\text{ if } 6|(7^k-1) \text{ for some positive integer k , then } 6|(7^{k+1}-1) \]