Write the sum

- 4 + 16 – 25 + ...

using summation notation.

Answer

The terms are squares, with alternating signs. The general term is

(-1)^{n + 1} *n*^{2}

and we want to start at *n* = 2.

In summation notation the series looks like this:

For these exercises, we'll give whichever answer we think is simplest. If you get something different, consult with a teacher or friend, because you may have a different and correct answer. Like coming up with new nacho topping combinations, there are infinite ways to write the same series.