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March 29, 2017

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Find a series ∑a_n for which ∑(a_n)^2 converges but ∑|a_n| diverges

  • Calculus - ,

    Consider
    1 - 1/2 + 1/3 - 1/4 + ... (alternating harmonic series)


    1 + 1/4 + 1/9 + 1/16 + ... = π2/6


    1 + 1/2 + 1/3 + 1/4 + ... diverges (harmonic series)

  • Calculus - ,

    thanks!!

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