$($p$-$series$)$ Determine whether each p$-$series converges or diverges.

$($a$)\backslash$sum$\_($k$=1)^(\backslash$infty $)(7)/($k$^(0\mathrm{.}9))$;

$($b$)\backslash$sum$\_($k$=1)^(\backslash$infty $)(-(1)/($k$^($c$)))$;

$($c$)\backslash$sum$\_($k$=1)^(\backslash$infty $)(3)/($k$)$;

$($d$)1+(1)/(2\backslash$sqrt$(2))+(1)/(3\backslash$sqrt$(3))+$cdots;