■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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