Ok so basically we are told about this comparison test which says if one series is greater or equal than another for all values, and converges, so does the second series. and if the first is less and diverges, the greater one diverges.

I want to know how does the comparison test show that

converges given

diverges?

This is the proof we are asked for but I don't see that there's enough information there. given the first is always less than or equal to the second, for all r, however the comparison test says that if the smaller series diverges, so does the bigger which contradicts this? please help, i am confused, this proof is integral to the rest of the questions and without this I can't procede with my work... S:

i dont see that the comparison test actually answers this