ÖFVERSIGT AF K. VETENSK.-AKAD. FÖRHANDLINGAR 189 3, N:0 0. 569 



Om man i eqvationen 



1 12 



Are tg - '—^ — Are tg — -^ = Are tg — 

 ö m — 1 m + 1 m- 



gör ra — 2, o, 4, . . . ra, så får man 



1 1 4 2 



Are tg T — Are tg ~ = Are tg - „ 



I 1,2 



Are tg g — Are tg ^ - Are tg p 



II 2 

 Are tg ^ — Are tg T = Are tg ^ 



Are tg m i_ g - Are tg 4 = Are tg ^-4-^ 



1 1 4 2 



Are tg — - — Are tg T = Are tg — = . 



B m — 1 m + 1 w 2 



Genom addition finner man 



y = ni 



111 c — N 2 



Are tg T + Are tg - — Are tg Are tg— — r == Si Are l § 5s : 



ö 1 "2 m m + 1 h-J V 



men nu är 



Are tg y + Are tg ^ = Are tg o , 



1 1 . 2m + 1 



Are tg— + Are tg f — Are tg — _— -^ , 



& m fe ra + 1 w« + m — 1 



alltså blir 



S2 o A 2m + l 

 Arc tg - = Are tg o — Are tg -^- — T . 



i' = 2 



2 

 Om man på båda sidor tillägger Arctgy^, samt öfvergår 



till dim. för m=<=©, så fås 



2 



Arctg- 2 = Arctg(— 1)= T 



