■互いに素となる整数(その5)

 (その2)を補足.

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  1/1^2+1/3^2+1/5^2+1/7^2+1/9^2−・・・=π^2/8

  1+1/9+1/25+・・・

=1+1/4+1/9+・・・−1/4(1+1/4+1/9+・・・

=ζ(2)−ζ(2)/4=π^2/8

 なお,カタラン定数G:

  G=1/1^2−1/3^2+1/5^2−1/7^2+1/9^2−・・・=0.911・・・

  2(1/1^2+1/5^2+1/9^2+・・・)=π^2/8+G

  2(1/3^2+1/7^2+1/11^2+・・・)=π^2/8−G

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