Hi Am working through heaps of series problems in which i'm expected to show the series converges or diverges by applying both root and ratio test,
For the series;
I went ahead and applied to ratio test getting;
limit as n --> inf of 2/(n+1) = 0 hence 0 < 1 means convergence,
but i then applied the root test and ended up with;
lim as n--> inf of 2/((n!)^(1/n)) which i figured to be = 2/1 hence > 1 and divergent,
Clearly i ahve stuffed one of these up and i'm a bit sketchy with limits so could be there but can someone tell me which i've stuffed up and how?
Many thanks in advance.