It is true that .
But what about
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.