Second rule of comparison in math series

[Alem2000]

I can't understand this \sum{A_n}\leq \sum{B_n} having said this

if \sum{B_n} converges so does \sum{A_n}, okay that

makes perfect sense but then the second rule of comparison is if \sum<br /> <br /> {A_n} diverges then so does \sum{B_n} diverges too...can

anyone tell me how that makes sense? A proof maybe..?

 

[matt grime]

General result, if P implies Q, then not Q implies not P.

replace P with sum Bn converges and Q sum An converges.

 

[HallsofIvy]

Or:

Given \sum{A_n} does NOT converge.

Now assume \sum{B_n} DOES converge. Using the theorem you said "makes perfect sense", what does that tell you about \sum{A_n}
?