| if |
|
|
lim
n® ¥
|
|
an
bn
|
= L where L is finite and positive |
|
| | then either both series |
|
|
¥
å
n = 1
|
an and |
¥
å
n = 1
|
bn converge or they both diverge. |
|
|
| if |
|
|
lim
n® ¥
|
|
an
bn
|
= 0 and |
¥
å
n = 1
|
bn converges then |
¥
å
n = 1
|
an also converges |
|
| and if |
|
|
lim
n® ¥
|
|
an
bn
|
= ¥ and |
¥
å
n = 1
|
bn diverges then |
¥
å
n = 1
|
an also diverges |
|
|