If what we want is a function that will compute the sum of the first n
integers, what is unsatisfactory about our answer?

Click here for the answer.

What we have is an expression, not a function. If we want to use
this expression to solve a particular problem---such as finding the sum of the
first 100 integers---we have to type it back in, using 100 in place of n.
This isn't too bad in the present case since the expression is so simple, but
it would be a major pain with a complicated formula.