Chapter 11 - Infinite Series - 11.2 Summing and Infinite Series - Exercises - Page 547: 4

$S_{2}$ = $-\frac{1}{2}$ $S_{4}$ = $-\frac{7}{12}$ $S_{6}$ = $-\frac{37}{60}$

$S_{2}$ = $(-1)^{1}·1^{-1}+(-1)^{2}·2^{-1}$ = $-\frac{1}{2}$ $S_{4}$ = $(-1)^{1}·1^{-1}+(-1)^{2}·2^{-1}+(-1)^{3}·3^{-1}+(-1)^{4}·4^{-1}$ = $-\frac{7}{12}$ $S_{6}$ = $(-1)^{1}·1^{-1}+(-1)^{2}·2^{-1}+(-1)^{3}·3^{-1}+(-1)^{4}·4^{-1}+(-1)^{5}·5^{-1}+(-1)^{6}·6^{-1}$ = $-\frac{37}{60}$