APPENDIX VI. 399 



C = I'Qj^" ^ -R 



" -,_ J_ l-Op"-l* 



C.= ^^+ ^' + ^^ + ... -^ 



Here a = ,-^; ; g = —7-— ; and ;i = 00 ; hence, 

 1-O^y" -^ 1-0^;" ' 



B 

 " 1 _ 1 l-0»" - 1 ' 



Funnuld X. — C'„ — ',7^-- — y- is obtained l)y multiplying 

 Fonnula VIII. by l-O^;"; or in the following way : — 

 c: = 11 + -IL- + JL, + . . . + A_ 



P 



Fonuida XI. — /• = _ ^ — - x -Op 

 l-0/j"-l 



11 . B, . r . r 



+ 4-. ..00= + +...00' 



l-Qp" ^ 1-0/" ^ 1-Qp ^ l-Qp- ^ 



or, according to Formulas VIII. and VII., 



Formula XII.— r = - ^ x l-Qjj"-'" ^ .^ 

 1-Op" — 1 



or, according to Formulas IX. and VII., 



B X l-Oj)"-'" r T B X 1-Op"-'" ^, 



