Also the numerator oscillates back and forth between +1 and −1; it is +1 when k is odd
and −1 when k is even. To achieve this oscillation, insert a factor of (−1)k+1 (or (−1)k−1)
into the formula for ak . [For when k is odd, k + 1 is even and thus (−1)k+1 = +1; and when
k is even, k + 1 is odd and thus (−1)k+1 = −1.] Consequently, an explicit formula that
gives the correct first six terms is