If I have [tex] (a_n + b_n)^n = c_n [/tex] where a_n is convergent and b_n divergent. Is c_n then divergent? And what if a_n and b_n were divergent, would c_n be divergent also? but what if they were both convergent then surely c_n is convergent right? I can't see a rule or a theorem that tells me this is correct and frankly it is getting on my nerve. Somebody here who knows? Thanks.