- #1

vrbke1007kkr

- 10

- 0

## Homework Statement

Assume all s

_{n}=/= 0, and that the limit L = lim|(s

_{n+1})/(s

_{n})| exist.

a) Show that if L<1 then lim s

_{n}= 0

b) Show that if L>1 then lim s

_{n}= + oo

## Homework Equations

There is a hint that we should select 'a' s.t. L<a<1 and obtain N s.t. n>N => |s

_{n+1}< a|s

_{n}|.

Then show that |s

_{n}| < a

^{n-N}|s

_{N}|

## The Attempt at a Solution

Its easy to get: |s

_{n+1}|< ([tex]\epsilon+L[/tex])|s

_{n}|, now I tried using the fact that L<1 to find an epsilon and an 'a' such that |s

_{n+1}|< a|s

_{n}|

Even if I find such a, and even if I can prove |s

_{n}| < a

^{n-N}|s

_{N}|, how do I get that |s

_{n}| < [tex]\epsilon[/tex] for all epsilon