Say that
Let then
As noted
You can fill in the details and finish.
Let and be two sequences in such that and both of which converge. Show that and converge.
Hint: let
I'm able to show that if and converge then and both of which converge.
for this I'm not sure if it's:
if I use the hint I'm back to were I started, which is basically at the beginning, and have no clue how to precede.