If Xn->X (in probability) and Yn->Y(in probability) and Cn=Xn+Yn and C=X+Y show that Cn->C (in probability).
what i got so far
|Xn-X|<=ε/2 and |Yn-Y|<=ε/2
so lim(n->inf) P(|Cn-C|>=ε)=0
I want to verify if this is correct, and if not, what's the mistake, or if I am missing anything.