SLR LA TRANSFORMATION DES SÉRIES. 21 



28. Pour passer au calcul numérique , soient d'abord 



d„ = (-2n — I) (2m + I) 2 (2w + 5) 2 (2n h- 5) 2 (2m + 7), 

 d n+l = (2w + I) (2m + 5) 2 (2m + 5) 2 (2m h- 7) 2 (2« + 9); 



d'où 



(2m -4- 7) (2« + '.)) 



L.. = rf„ 



"(-2)i— I) (2m -4- 1) 



Partant de (/, , et appliquant cette relation , on l'orme le tableau suivant : 



d, = 5 2 5 2 .7 2 .9 = 99 225, 



9.11 



,/., = </, = </,.35 = 5 274 425, 



5 



11.15 



,/, =</., = 218 29o.l45==51 21(5 185, 



5.5 



,1. =(/, "' J = 4 459 455.59 =175 918 745, 

 5.7 



, 15.17 

 ,/, = d i = 8 281 8i5.85 = 703 956 825, 



7.!» 



17.19 

 ,/,. = f / 5 -—- = 7 110 675.17.19 = 2 296 748 025, 



, 19.21 



,/, = f / = 16 061 175.19.21 = 6 408 408 825, 



11. 13 



21 .23 ' 



,/ 8 =,/, = 98 590 905.161 =15 875 155 705, 



13.15 



25.25 



d 9 =rf 8 — =511 257 955.115 = 55 792 564 825, 



15. 17 



d l0 = (h ^-^-= 110 812 275.675 = 74 798 285 625, 



ç>7 99 

 d.. = d w — — = 562 595 125.261 = 146 784 605 625, 

 19.21 



ç>q -;| 



iLsi,- — = 503 901 875 899 = 275 207 785 625, 

 12 "21.25 



d a = d ti ' =475 145 975.1 025 = 486 072 286 425, 

 25 . 25 



,/,, = (/„ 0a ' at) = 10 801 606 565.77 = 851 725 690 105, 

 25.27 



