## Algebra and Trigonometry 10th Edition

$a_n=(-1)^n\frac{n+1}{n+2}$
The signs are alternating (starts with negative). The numerator starts at $2$ and increases by $1$ at each term, and the denominator starts at $3$ and increases by $1$ at each term. Thus a general term is $a_n=(-1)^n\frac{n+1}{n+2}$