# Calc1.11

From Example Problems

Evaluate .

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 .