Question

using mathematical induction prove the following?
6n-1isdivisible by 5,for n>0 ?

Answer 1

Clearly, 6*2 - 1 = 12-1 = 11
is not divisible by 5.
So, I assume you meant 6^n - 1 is divisible by 5.
Check P(1):
6^1 - 1 = 6-1 = 5, is divisible by 5. So, P(1) is true.
Assume P(k). Then
6^(k+1) - 1 = 6*6^k - 1
= 5*6^k + 6^k - 1
Now, we know that 6^k - 1 is a multiple of 5, say 5m
So, 5*6^k + 5m = 5(6^k+m) is divisible by 5.
So, we have P(1) and P(k) ==> P(k+1)
so, P(k) is true for all k > 0.