If the series of an and the series of b are positive term series for which series an converges and series bn diverges. Would series an*bn converge, diverge, or does it have not sufficient information?

Question

If the series of an and the series of b are positive term series for which series an converges and series bn diverges. Would series an*bn converge,  diverge, or does it have not sufficient information?

misty1212 · Answer

HI!!

misty1212 · Answer

lets try a couple examples

misty1212 · Answer

$$\sum\frac{1}{n^3}$$ converges right ?

misty1212 · Answer

this is where you say "yeah it does"

anonymous · Answer

Yup!

misty1212 · Answer

and how about 
$$\sum n$$

anonymous · Answer

diverges, it does to infinity

misty1212 · Answer

multiply and get $$\sum\frac{1}{n^2}$$ converge or diverge?

anonymous · Answer

converge

anonymous · Answer

But that is only one example....

misty1212 · Answer

right but now at least we know it CAN converge 
now try it with 
$$\sum\frac{1}{n^2} , \sum n^2$$

anonymous · Answer

converge once again!

misty1212 · Answer

oh no!

misty1212 · Answer

$$\frac{1}{n^2}\times n^2=1$$ and $$\sum 1$$ does not converge

anonymous · Answer

Wait I mean diverge since it is a positive term

anonymous · Answer

Divergence test shows that it goes to infinity.

anonymous · Answer

Okay so we showed it could be divergent of convergent.... so this is not enough information?

anonymous · Answer

Okay, thank you!

misty1212 · Answer

yeah it totally depends on each 
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