Investigate the convergence of $ \sum_{n=1}^{\infty } (-1)^{n}\frac{n+2}{n(n+1)} $ I am supposed to investigate the convergence of $ \sum_{n=1}^{\infty } (-1)^{n}\frac{n+2}{n(n+1)} $. I'm unsure whether to use Leibniz' criterion or a comparison test and I really can't start. Thanks

Hint:
$$
{{n + 2} \over {n\left( {n + 1} \right)}} - {{n + 3} \over {\left( {n + 1} \right)\left( {n + 2} \right)}} = {{n + 4} \over {n\left( {n + 1} \right)\left( {n + 2} \right)}}
$$
