Find the limit of the sequences: $a_{n+1}=3a_n - n + 1$ and $(a_n)^\frac{1}{n}$ with $a_0 > 0 $ Let $a_0 > 0 $ and $$a_{n+1}=3a_n - n + 1.$$
I have to find its limit. I have also to find the limit of $(a_n)^\frac{1}{n}$. But this seems even more complicated. For the first part I've used the comparison $$a_n>\frac{n-1}{2}$$ and I've got that the limit is $\infty$.But I've no clue about the second limit. 

You can find exactely what the solution to that reccurence is ($A\cdot3^n+\frac{1}{2}n-\frac{1}{4}$) and than just calculate the limit. 
