i know that An->1
i need to prove that (An)^n ->1
but when i construct limit
lim (An)^n
n->+infinity
i get 1^(+infinity) which says that there is no limit
what do i do in this case in order to disprove that (An)^n->1
??
Why not try this method? Your book ought to show that the Root and Ratio test always yield the same result. So
And you have already asked this question already.
Also let us try a three case scenario again
Case #1:
It is clear then from the fact that that there exists some such that [tex]N\leqslant{n}[/math[ implies
From there it is clear then that
Or
Case #2:
From here it is clear that there exists a such that implies
And it should be clear then that
Or
Case #3: This is when where the conclusion readily follows.