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Math Help - subsequences

  1. #1
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    subsequences

    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
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bigb View Post
    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

    CB
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