Find the sum S = 1 + 3 + 5 + · · · + 13 + 15 = X 7
n=1
(2n + 1) by doing the following:
Copy down the series S in increasing order.
Underneath this, write the series S in decreasing order.
Add the two lines by adding the pairs of numbers in each column.
Simplify the result. [Hint: Determine how many terms are being added together
on the right hand side.]
Solve for S.