Denote and then, as . Being convergent, also is convergent.
Remark: This is a particular case of the Bertrand series.
I have the following series . I used the integral test, but since the function has a maximum at e not sure if its the right test. I got 2/e which is < 1 hence the series converges.
Thanks, for all thelp..
Echoing Danny's comments, the more general requirement for the intergral test is that there must exist some N such that, for all , . That is, it only matters that the "tail" of the sequence is positive.