Chapter 1.4, Problem 7P

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).

$\frac{3}{1\cdot 2}-\frac{5}{2\cdot 3}+\frac{7}{3\cdot 4}-\frac{9}{4\cdot 5}+\mathrm{...}$