Rewrite each of the following sums using summation notation.

1. $5 + 7 + 9 + 11 + 13$

   Hint (a):

   Answers vary. Here are three possible answers.

   $\displaystyle\sum_{n=1}^{5}2n+3 \ \ \ \ \sum_{n=5}^{9}2n-5 \ \ \ \ \sum_{n=0}^{4}2n+5$

   Notice the index of all answers: every index has exactly $5$ terms... because there are exactly $5$ terms in the series.

2. $2\cos(2\pi) + 3\cos(3\pi) + 4\cos(4\pi) + 5\cos(5\pi)$

   Hint (b):

   Complete the argument:

   $\displaystyle \sum_{n=2}^{5}$

3. $\frac { 1 } { 5 } f ( - 2 ) + \frac { 1 } { 5 } f ( - 1 ) + \frac { 1 } { 5 } f ( 0 ) + \frac { 1 } { 5 } f ( 1 ) + \frac { 1 } { 5 } f ( 2 )$

   Hint (c):

   Complete the index:

   $\displaystyle \sum_{k= }^{?}\frac{1}{5}f(k-2)$