Hello. I have a problem. I dont know how to finish my proof. Maybe someone of you will be able to help me. So task is: Suppose that fn and gn are function of the sequence. fn simply convergence(? dont know if english term is same) to f, and gn simply convergence to g. Need to prove that gn*fn convergence to g*f. my attempt: for every ε1 there is N1 that |gn-g|<ε1 for every ε2 there is N2|that fn-f|<ε2 so i need to prove that |fn*gn-f*g|<ε. So I make a few alterations |fn*gn-f*g|=|(gn-g)*fn+g(fn-f)|< |(gn-g)fn|+|g(fn-f)|<|gn-g|*|fn|+|g|*|fn-f|... and dont know how to finish that... Maybe someone have a tip for me? Thanks.