Solution: First rewrite the summand as .
Then make the substitution .
Now call the sum , for notational purposes.
With this notation it follows .
Then recognize . Only here the indices have been reversed, first in name and then in order.
Adding the two previous expressions for gives .
But . So it follows that which is equivalent to .
So now all that is left is to evaluate , and call this . Now it follows from that .
Subtracting gives . So , and since it follows that .