BINOMINAL SUMMATION 105 



D'¥ = ZA^^A^ + 6AiA.,Ai + 3^ 1^3- + 3^2-^3, 



D'b' = 3AM^ + 6AiA.zA, + GA^A^Ai + SAMa + 3^ 2^3', 



D^¥ = 4 AM i + nAM2Az + 4^l^2^ 



2)4^4 = 4^j3^, + UAMoAi + 6^1^32 + UAiAMs + ^2', 



m^ = 5AM2, Db' = 6AM2, 



D'b'' = 5AMs + 10AM2\ D'b' = GAMs + 15^1^22, 



D'b' = 5AMi + lOAM^As + lOAM-/, Db'' = 7AM2. 



To illustrate the use of the procedure given above, let us evaluate 

 Ri. We have 



-(l/6)(5/2)(7/2)(9/2Mo-"'^(3^iM2) 



+ (l/24)(5/2)(7/2)(9/2)(ll/2Mo-^^/Mi'' 

 or 



R, = (5/2)^o-T- AM, + (7/2)^o^(.4i^3 + A,y2) 



- (l/2)(7/2)(9/2Mo^iM2 



+ (l/24)(7/2)(9/2)(ll/2M,'']. 



Tables Indicating Degree of Accuracy Obtainable by 

 Use of Formula (3) for Evaluating 



p-l{:)p<^-pr 



Pi = 1st approximation, Ai = (P - Pl)10^ 

 Po = 2d approximation, Ao = (P - P2)10«, 

 P3 = 3d approximation, A3 = (P - P3)10^ 

 a = np, 



T^ = (n - 1) log-^ + (c - 1) log^^^ + (n - c) log 

 n — 1 d 





e-"dl. 



