Question

prove that
lim [a power 1/n] =1 for a>0​

Answer 1

Answer:

The question is incomplete:

Prove that

∙ for |a|<1,limn→∞an=0

∙ for |a|>1,limn→−∞an=0

For |a|<1

b=1a,|b|>1

limn→∞an=limn→∞(1b)n=limn→∞1bn=1±∞=0

For |a|>1

x=−n

limn→−∞an=limx→∞a−x=limx→∞1ax=1±∞=0