Limits of products involving limsup and liminf

[Ed Quanta]

So suppose an approaches L,

then how do I know that the statement

1)If lim supbn<b, then limsup(anbn)<Lb

implies that

limsup(anbn)<=L*limsup(bn)

is true?


2)How do I know that

limsup(anbn)=L*limsup(bn)

implies

liminf(anbn)=L*liminf(bn)

is true?

 

[mathwonk]

i suggest you go back and read what some of us said in answer to your previous post. you want to get some skill with this idea yourself. the methods are the same.

 

[Ed Quanta]

Thanks dude. I'll look back.