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Math Help - Convergence of Subsequences

  1. #1
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    Convergence of Subsequences

    Construct a sequence xn (from one to infinity) such that it contains one subsequence that converges to 1 and another subsequence which converges to 0.
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  2. #2
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    Re: Convergence of Subsequences

    Hi renolovexoxo,

    The easiest way to construct such a sequence is to define all the even terms as one and odd terms as zero (or vice versa).

    x_n=\begin{cases}1&\mbox{ if }n=2k\mbox{ where }k\in\mathbb{Z}^{+}\\0&\mbox{ if }n=2k+1\mbox{ where }k\in\mathbb{Z}^{+}\cup\{0\}\end{cases}
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