Determine convergence or divergence by any method.

$\backslash$sum$\_($n$=0)^(\backslash$infty $)((-1)^($n$)$n$)/(\backslash$sqrt$($n$^(2)+9))$

The series

diverges, since $\backslash$lim$\_($n$->\backslash$infty $)$a$\_($n$)!=0.$

converges, since the terms are smaller than $(1)/($n$).$

converges, since $\backslash$lim$\_($n$->\backslash$infty $)$a$\_($n$)=0.$

converges, since the terms alternate.

diverges, since the terms are larger than $(1)/($n$^(2)).$