Chapter 1.4, Problem 6P

For the following series, write formulas for the sequences a_n, S_n, and R_n, and find the limits of the sequence as $n\to \infty$ (if the limits exist).

${\displaystyle \underset{1}{\overset{\infty }{\sum }}\frac{1}{n(n+1)}}Hint:\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}$