> 
> Show that $a\_n=n^2+n+1$ satisfies
>  \begin{cases}
> a\_0=1\\
> a\_k=a\_{k-1}+2k & \text{for $k>0$}
> \end{cases}
> 
> 
> 

I want to use induction to solve this problem. but I don't know what my base will be since $k$ has to be greater than $1$. Should my base case be when $k=1$ (assuming this question uses integers). 

Please give me a hint on how to solve this.