Prove by induction: $3^n+1$ is divisible by $2$ for $n\ge 0$ I'm going through the process of induction and when I'm attempting to prove $P_{k+1}$ I keep getting $2(3A-\frac32)$, where $A$ is an integer and $A\geq 1$, which isn't possible since $3A-\frac32$ should be an integer.
My method is to write $P_k$ as $3^k+1=2A$, where $A$ is an integer and $A\geq 1$. Then for $P_{k+1}$ I write $3^{k+1}+1=2A$ and then I try to make the $LHS$ equal to the RHS.
Where am I going wrong?

For $k+1$, you already assume that $3^k + 1 = 2n$ for some integer $n$. Then, use the fact that
$$3^{k+1} + 1 = 3\cdot 3^{k} + 1$$
and substitute $3^k$ with the expression above.
