Compare the accuracy of four approaches to the similar convergent alternating series                          Sn = 1 − 1/2 + 1/3 − 1/4 + 1/5 − 1/6 + 1/7 − 1/8 +···+ (−1) n+1 /n, where limn→∞ Sn = loge...

Compare the accuracy of four approaches to the similar convergent alternating series

                         Sn = 1 − 1/2 + 1/3 − 1/4 + 1/5 − 1/6 + 1/7 − 1/8 +···+ (−1) n+1 /n,

where limn→∞ Sn = loge 2.

(a) Add from largest to smallest (1 to n).

(b) Add from smallest to largest (n to 1).

(c) Add the pairs first: (1 − 1/2) + (1/3 − 1/4) +··· .

(d) Add the pairs analytically: sum 1/((2k − 1)(2k)) from k = 1.