In parts (a)-(d), find the values of the sums in terms of $n$. In part (e), evaluate the limit of the sum from part (d).

1.    $\displaystyle \sum_{k=1}^{n} k =$
   
   
2.    $\displaystyle \sum_{k=1}^{n} \frac{k}{n^2} =$
   
   
3.    $\displaystyle \sum_{k=1}^{n} \frac{6}{n} =$
   
   
4.    $\displaystyle \sum_{k=1}^{n} \left( \frac{3 k}{n^2} - \frac{6}{n} \right) =$
   
   
5.    $\displaystyle \lim_{n\to\infty} \left( \sum_{k=1}^{n} \left( \frac{3 k}{n^2} - \frac{6}{n} \right) \right) =$