I need some help with proving a theorem. I really appreciate any kind of help.
Theorem: Suppose [an] is a convergent sequence and sigma un is a convergent positive series, then sigma ((an)^2)(un) is convergent.
The n's in an and un are subscripts.
Maybe I understand it wrong but it seems true, and not really difficult... Since is convergent, is convergent as well, hence it is bounded: there is such that for all . From there, we deduce and you can conclude.