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

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