Posted by Timofey on Saturday, August 11, 2012 at 11:21am.
Prove via Mathematical Induction that
(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?

Calculus  Steve, Saturday, August 11, 2012 at 12:50pm
It's obviously not true.
7*21 = 13 which is not divisible by 6
I think you mean 7^n1 is divisible by 6
when n=1, 7^11 = 71 = 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^k1) + 6
but, 7^k1 is divisible by 6, and 6 is divisible by 6, so 7(7^k1)+6 is divisible by 6
since 6a+6b = 6(a+b)
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