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Math Help - any example of sequences that their series satisfy these conditions

  1. #1
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    any example of sequences that their series satisfy these conditions

    \sum{x_{n}^{2}} and \sum{y_{n}^{2}} converge. But:

    \sum{(x_{n}+y_{n})^{2}} does not converge.
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  2. #2
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    \sum (x_n+y_n)^2 converges if and only if \sum x_n^2+y_n^2 + 2x_ny_n converges if and only if \sum 2x_ny_n.

    But |2x_ny_n| \leq x_n^2+y_n^2.
    And \sum x_n^2+y_n^2 converges.
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