Proof by induction that $3^n - 1$ is an even number How to demonstrate that  $3^n - 1$ is an even number using the principle of induction? 
I tried taking that $3^k - 1$ is an even number and as a thesis I must demonstrate that $3^{k+1} - 1$ is an even number, but I can't make a logical argument. 
So I think it's wrong the assumption... 
Thanks

Hint: try substituting back in $3^k = 2x+1$
