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...