■ある無限級数(その44)

  1+1/2+1/3+1/4+・・・=∞

  1−1/2+1/3−1/4+・・・=log2  (条件収束)

に対して

  1+1/2+1/4+1/8+・・・=2  (絶対収束)

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  S=1+1/2+1/4+1/8+・・・

 2S=2+1+1/2+1/4+1/8+・・・

   =2+S

  S=2

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  S=1+2+4+8+・・・  (発散級数)

 2S=2+4+8+16+・・・

   =S−1

  S=−1

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