Prove via Mathematical Induction that

Question

(7*n) - 1 is divisible by 6.

I have that it is divisble when n=1, but not n=2 and so on. How should I write the inductive proofs?

Answer 1

It's obviously not true.

7*2-1 = 13 which is not divisible by 6

I think you mean 7^n-1 is divisible by 6

when n=1, 7^1-1 = 7-1 = 6 is divisible by 6
assume for n=k
when n=k+1,
7^(k+1)-1 = 7*7^k - 1
= 7*7^k -7 + 6
= 7(7^k-1) + 6
but, 7^k-1 is divisible by 6, and 6 is divisible by 6, so 7(7^k-1)+6 is divisible by 6

since 6a+6b = 6(a+b)