Evaluate limn→∞(12)nn=limn→∞ann\lim_{n \to \infty} \sqrt[n]{\left(\frac{1}{2}\right)^n} = \lim_{n \to \infty} \sqrt[n]{a_n}limn→∞n(21)n=limn→∞nan for the root test applied to ∑n=1∞(12)n\sum_{n=1}^{\infty} \left(\frac{1}{2}\right)^n∑n=1∞(21)n.
000
12\frac{1}{2}21
111
∞\infty∞