AlIAE NONNOLLAE APPI.ICATI0NE5 ETC. 5j3 



rn— 2n r n— 5 n\ "—2 



an — 8 -| r n — 9 -i f n — 8 -i f n — g -,>. i 



10)^...H-1C3)J-+.Ll(1)-H...-4-1(i)J-HLl(')^...^1(4)J_HLia)H-...-4-1(5)J> 



Ista aequalitas in hunc modum transforraari qucit 



U„= { [IC )]/" _(["lTl )]-(-[1 OVI (3)])S ""-+-([1 ( ")Ih1 (5)]-t-[1 ('"-ill (3)])2"~^ 



_([1(i)_^7.-4-1(3)]-H[1(0^r~'H_1(')]}3""lH ) .s 



n — 2 n — 3 M — 4 n—4 n — 4 



— [[W]z _-(i:i(')]-H[1(')-4-1(-')])2 -f. ] , 



quae ad banc reduci evidenicr potest 



U,.=Un_,.=— Un_2. 



Sub tali aspectu praecedens aequatio theorema comprehendit 

 simile iheotemati^ quod iu forinnla (C) continetur. 



Si formula (A) icsumuur, atque derivata prima deduci- 

 lur, utroque membro per n z niultiplicato, erit 



pi — 1^ n — 1 p n — 2 -, n — 2 p n — 3 -i n~3 



^'S„=7l.S'„z^-nL1(■)> — 2n[l{')-Hl(^)> _3n[l(')-Kl(2)Jz 



tn — 1 -, n — 4 p n — 5 - n — 5 

 . 1(0-1-.. .^10)Js h_5«[i(0_h...-h1W> — 



Ex eadem formula (A) cum eliam profluat 



r- n -. n — 1 pH — i-. n— 2 p n — 2 -j n— 1 



S'„_wLl(0> _(«_i;[i(i)j3 _h(„_2)[i(')h-1(2)> 



r n — 3 -. n — 4 



-H(«— 3,Ll(')-t-1.(2)Js _ =0, 



SI primum hujus aequationis mcmbrum addalur secundo ae- 

 quatioiiis praecedenlis, babebimus 



