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  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Sequence...

    Let (a_n)^\infty_{n=1} converges to a.

    Is the next sequence b_n also converges?

    b_n=\frac{a_1^2+a_2^2+\dots +a_n^2}{n}


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  2. #2
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    Quote Originally Posted by Also sprach Zarathustra View Post
    Let (a_n)^\infty_{n=1} converges to a.
    Is the next sequence b_n also converges?
    b_n=\frac{a_1^2+a_2^2+\dots +a_n^2}{n}
    Do you know the idea of the sequence of means?
    Because \left(a_n\right) converges it is true that \left(a_n^2\right) also converges.
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