Recent content by nevnight13

Here is my attempt...: case 1: bk<1 then 1+bk<2 so bk/(1+bk) > bk/2 so and Ʃ[bk/2] diverges so by comparison Ʃ[bk/(1+bk)] diverges case 2: bk>=1 then 2bk>bk+1 so Ʃ[bk/2bk] < Ʃ[bk/(1+bk)] -->Ʃ[1/2] < Ʃ[bk/(1+bk)] since Ʃ[1/2] diverges...

Sorry but is there anymore guidance you could give? I keep failing at comparison and ratio test doesn't seem to work because we do not know if bk is decreasing, increasing or oscillating.

Homework Statement let bk>0 be real numbers such that Ʃ bk diverges. Show that the series Ʃ bk/(1+bk) diverges as well. both series start at k=1Homework Equations From the Given statements, we know 1+bk>1 and 0<bk/(1+bk)<1 The Attempt at a Solution I've tried using comparison test but cannot...