Write the following sums in expanded form.

1.  $\displaystyle \sum _ { n = 3 } ^ { 7 } 4 n - 7$

   Answer (a):

   ${\displaystyle\sum\limits_{\textit{n}=3}^{7} 4\textit{n} - 7 = (4.3 - 7) + (4.4 - 7) + (4.5 - 7) +(4.6 - 7) + (4.7 - 7) = 5+9+13+17+21}$

2.  $\displaystyle \sum _ { j = 2 } ^ { 8 } ( - 1 ) ^ { j }$