Give an example of sequences {an}, {bn}, such that {an} is bounded and {bn} is convergent but {an+bn} and (an*bn} are divergent. I chose {an} = 1/n^2 since 0

Question

Give an example of sequences {an}, {bn}, such that {an} is bounded and {bn} is convergent but {an+bn} and (an*bn} are divergent. I chose {an} = 1/n^2 since 0<(1/n^2) <= 1. I'm having trouble coming up with a {bn} that would satisfy the last two properties.

tiffany_rhodes · Answer

Maybe I should take {(-1)^n} to be my an since it would be bounded between -1 and 1?

tiffany_rhodes · Answer

so for {an} = (-1)^n and {bn} = n/2n+1. Does this look reasonable? I'm trying to verify that the last two sequences would be divergent

zarkon · Answer

how about $b_n=1$  

 make it easy

tiffany_rhodes · Answer

why do I have to make things exponentially more difficult? I'll try that and make sure I can prove that they would be divergent