Here's something I thought would be easy to prove (if I'm corret of course)

If -> x and x >a, then for infinitly many values of n.

My working: we need for n sufficently large

->

whatever I do I can't seem to deduce x_n > a for all but finite n

My second question is very simple. In the ratio test, if the limit does not exist what does limit superior greater than 1 imply?

Thanks.