prove that the limit of the sequence an=1/n+1/(n+1)+...+1/2n exists. show that the limit is less than 1 but not less than 1/2. the first part of the question i did already, im not sure about the second part of the question if i did properly. n(1/n+...+1/2n)>=an=1/n+...+1/2n>=1/n^2+...+1/2n^2 because the limit exists, for every n>N(e) (for every e>0) |a-an|<e and thus, a-e<an<a+e if we let e=1/2 then a+e<=1.5 and thus a<=1. a-1/2>=1/n^2+...+1/2n^2-1/2>0 thus a>1/2. is this correct? thanks in advance.