Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises - Page 601: 46

$S_1=-\log 2$ $S_2=-\log 3$ $S_3=-\log 4$ $S_4=-\log 5$

Using the property of logarithms, $a_n=\log n -\log (n+1)$. $S_1=a_1=\log 1 -\log 2 =-\log 2$ $S_2=a_1+a_2=(\log 1-\log 2)+(\log 2-\log 3)=-\log 3$ $S_3=a_1+a_2+a_3=(\log 1-\log 2)+(\log 2-\log 3)+(\log 3-\log 4)=-\log 4$ $S_4=a_1+a_2+a_3+a_4=(\log 1-\log 2)+(\log 2-\log 3)+(\log 3-\log 4)+(\log 4-\log 5)=-\log 5$