# Second rule of comparison in math series

1. Nov 4, 2004

### Alem2000

I cant 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 $$\sum {A_n}$$ diverges then so does $$\sum{B_n}$$ diverges too...can

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

2. Nov 4, 2004

### 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.

3. Nov 5, 2004

### 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 $$\sum{A_n}$$
?