Show that if lim(an+1/an)>1 there exists a natural number such that lim(an+1/an)=>1+1/n.
I have been trying this, but I cant seem to get the proof?
Any Ideas? Thanks
Ok. I understand what Raabe's test is. I am just wondering if your problem is not what it seems. I literally interpreted your question as if $\displaystyle \lim\text{ }\left|\frac{a_{n+1}}{a_n}\right|>1$ then there exists some $\displaystyle n'\in\mathbb{N}$ such that $\displaystyle \lim\text{ }\left|\frac{a_{n+1}}{a_n}\right|\geqslant 1+\frac{1}{n'}$