Yes, there are many people who can do that. But the important thing is, can you?
In order to show that \(\displaystyle (a_n+ b_n)\) converges to a+ b, you must show that "given \(\displaystyle \epsilon> 0\) there exist N such that if n> N, \(\displaystyle |(a_n+ b_n)- (a+ b)|<\epsilon\)". You know that \(\displaystyle a_n\) converges to a so you know that "given \(\displaystyle \epsilon> 0\) there exist \(\displaystyle N_1\) such that if \(\displaystyle n> N_1\), \(\displaystyle |a_n- a|<\epsilon\)" and you know that \(\displaystyle b_n\) converges to b so you know that "given \(\displaystyle \epsilon> 0\) there exist \(\displaystyle n> N_2\) such that if \(\displaystyle n> N_2\), \(\displaystyle |b_n- b|<\epsilon\).
It will help to know that \(\displaystyle |a_n+ b_n- (a+ b)|= |(a_n- a)+ (b_n- b)|\le |a_n- a|+ |b_n- b|\). You should have had that inequality, \(\displaystyle |a+ b|\le |a|+ |b|\) before.
