I have the set $A=\left\{1+\displaystyle\sum_{i=1}^n (3-(-1)^i)\;\text{ where }\;n\in\mathbb{N}_0\right\}$ and I have to prove equality with $B=\{x\in\mathbb{N}\;\text{ where }\;2 \text{ and } 3 \text{ are not factors of }x\}$ and my first thought was to transform the sum to get a function which returns the numerical value $f(n)\in\mathbb{Z}$ based on the parameter $n$. But I don't know which methods i can use to "transform" or "expand" this sum (what is the right term for this kind of operation i want to do by the way?) - any short and hopefully easy description out there?
PS: Mathematica outputs $\displaystyle f(n)=\frac{1}{2}(6 n-(-1)^n+1)+1,n\in\mathbb{N}_0$ as the function i am searching for, but I don't know how to get to this result!