Complete the following problems about sigma notation.  

1. Expand the summation: $\displaystyle\sum _ { k = 1 } ^ { 4 } ( 3 k ^ { 2 } + 5 )$

   Step (a):

   $(3(1)^2+5)+(3(2)^2+5)+...$

2. Write the following using sigma notation: $0.2(4^3+4^{3.2}+4^{3.4}+4^{3.6}+4^{3.8})$

   Step 1(b):

   The argument (expression) is $0.2·4k^{x_k}$.

   Step 2(b):

   Write an expression for the '$x_k$'s.
   $x_k=3,3.2,3.4,3.6,3.8$ 

3. The sum in part (b) could be a left endpoint approximation of an area under a curve. Which curve? What is the interval?