Write $an$ inequality comparing $\frac{\sqrt[\phantom{2}]{n}}{n-6}$ with $\frac{1}{n^{\frac{1}{2}}}$ for $n7.$

$(Express$ numbers $in$ exact form. Use symbolic notation and fractions where needed.$)$

inequa

Determine the convergence $of$ the series ${\displaystyle \underset{n=7}{\overset{}{}}}\frac{\sqrt[\phantom{2}]{n}}{n-6}.$

The series diverges.

The series converges.

$It$ cannot $be$ determined whether the series converges $or$ diverges.