Let X=xn and Y=yn be given sequences, and let the shuffled sequence Z=zn be defined by z1:=x1, z2:y1,...z2n-1:=xn,z2n:=yn,... Show that Z is convergent if and only if both X and Y are convergent and Lim X=Lim Y
Let X=xn and Y=yn be given sequences, and let the shuffled sequence Z=zn be defined by z1:=x1, z2:y1,...z2n-1:=xn,z2n:=yn,... Show that Z is convergent if and only if both X and Y are convergent and Lim X=Lim Y
Use the fact that for a convergent sequence all subsequences converge to the same limit as the original sequence, and vice versa