First, some basic stuff about how to make maple evaluate sums.  Here's
how to tell maple to add n^2 for n =1, 2, 3, and 4.

> sum(n^2,n=1..4);

                                  30


Here's how to tell maple to add up the first 100 integers:

> sum(i, i=1..100);

                                 5050


As discussed in class, i is a "dummy variable".  In other words, it's just a
variable used for counting.  Replacing i with a variable of a different name
doesn't matter.

> sum(j, j=1..100);

                                 5050

>