【 級数式 】
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加法展開式を下記のように配置すると、第２項のみの無限級数式が得られる。
arctan(1/1) = arctan(1/2)
+ arctan(1/3)
arctan(1/2) = arctan(1/3) + arctan(1/7)
arctan(1/3) = arctan(1/4) + arctan(1/13)
arctan(1/4) = arctan(1/5) + arctan(1/21)
arctan(1/1) =
arctan(1/3) + arctan(1/7) + arctan(1/13) + arctan(1/21) + ・・・・・
π/4 = ∑arctan( 1
/ n＾2+n+1 ) | n=1,2,3,,∞
arctan(1/1) = arctan(1/3)
+ arctan(1/2)
arctan(1/3) = arctan(1/5) + arctan(1/8)
arctan(1/5) = arctan(1/7) + arctan(1/18)
arctan(1/7) = arctan(1/9) + arctan(1/32)
arctan(1/1) =
arctan(1/2) + arctan(1/8) + arctan(1/18) + arctan(1/32) + ・・・・・
π/4 = ∑arctan( 1
/ 2n＾2 ) | n=1,2,3,,∞