ALGEBRA. 3.3 



173. The sum of the first n coefficients of the expansion, in 



ascending powers of x, of -: , is 2"~* ~ ' . 



(1 - x) 6 



174. Prove that 



(n + 1) (n + 2) 

 ...4- 



17-".. Trove that 



a* (b c) 4- o \e a) 4- c** (fl bj 

 <** (6 c) 4- 6* (c o) 4- c* (a 6) 



is equal to the sum of the homogeneous products of n dimensions 

 of Oj b, c. 



XI. /.'.,-,, .nential and Logarithmic Series. 



us H?nlrr this head, n always denotes a po 

 whole number. 



Obtain the following equalities; 

 (1) n--(+l)(*-l)'+ *-2)'- ..... 1, 



(H~l)--n(u-2)-4-!^l ) (n-3)--... = [n- 1, 

 (3) ( W -2)--(n-3>^ tl ,-4)'-... = ln-n-2-, 



r-nr*r- , +(-ir(+ i)'a(-ir 



