' ■» 2 93 ===== 



Quare inter binos jhujus seriei coefficientes intervallo quo- 

 cunque zz r inter se remotos talis obtinet relatio, ut sit 



r ry -| 



— — — ■ ZZT ( 2/J -+ 2). (2fl -f- 3) (2B-+- 4) . t . . (2H+2r+l). 



[ Z . 11 -+ r ] 



J. 3. Lemmati huic sequentia subjungimus 

 Carollaria: 

 s) Si eompendii caussa ponatur 



(2 n-h 2 ) (2» -+- 3) zz: P 

 (2 /*+- 4) (2)1 •+- 5) =z Q. 

 (2 n-r- 6) (211 -+■ 7) zz: R 



( *ti -+■ 8)(2/i+ 9) = S 

 ( 2 n -+■ 1 o ) ( 2 /1 -+• 1 1 ) - T 

 (2/1-+- I2)( 2/2 -f- 13) = U &c. 



quarurn expressionum quaelibet, posito n -|- 1 loco n, abit 

 in proximam: patet, 



hincque posito n -+- 1 Ioco /j 



_ p . [Z£*£3 = ft . g^jgJ __ R . &c . 



posito 



r~i 



»* = 3 

 r = 4 



esse 

 [Z.n] 



[ Z . n -+ 1 ] 



EZ.»3 = p<Q [z.„ 



[Z.n-f-2] [Z.» + 3] 



[Z.n 



i] = . R .tZ^ = R.S;&c. 



3j [Z. »-+-4] 



JZ^ = P. a .R.[Z^] = Q.R. S ; L Z^] = RSX&c _ 

 [Z./Z-+-3J [Z./H-4.J [Z.«-+-5j 



^■'WaR.s/1^1 __ q . R . s . T; &c . 



[Z./z -h 4] 



[Z/Z-+5J 



2) Retentis iisdem valoribus P, Q, R, S &c.j facile 



demonstratur, esse 



( 2 n -+- 2 ) Q — ( 2 n -+- 1 ) . P ' zo ( 2 /z -+ 2 ) ( 1 o . (n -+- 1 ) 

 (2/1-+.445.R — (2/1-4-3)!. Qzz (2/1 -+-4) (10 (rz-+ 2) 

 ( 2 /1 -+- 6) . S — ( 2 n h- 5 j Rzr(2« + 6)(io ( rc -+- 3 ) 

 ( 2 /i -+ 8 ) T — ( 2 n -+ 7 ) S.'zz. ( 2 » -+■ 8 ) ( 1 o . . ( [n -+ 5 ) 



&c. 



7) 



7) 

 7) 

 7) 



et 



