Problem $3$

Complete the statement included beneath: Given that $\frac{1}{\sqrt[\phantom{2}]{n}}\frac{1}{\sqrt[\phantom{2}]{n1}}$ for $n1,$ and that $\underset{?}{lim}=-\frac{1}{\sqrt[\phantom{2}]{n}}=0$ the alternating infinite series $($with first term of value $1)$ must converge.