112 



AlvGEBRA. 



No 



I. 



Given. 



2. /, r, n, 



n, r, s, 



quired] 



Result, 



/, s, l—ar"-'] 

 I 



{r—i)s 





^= 





r, s, 



a, 71. s, r, /, 

 a, r, 



r, ?/, 



/, 71, 



a, 71, 





ar'' — a 

 r — I 



la"— I 



(r—i)sr"~^ 

 r"~i 



1 1 



/"-I— «"-i 



ar" — rs—a—s ; l^s—l)" '=a(s—a)" \ 

 a{s—ay-'=l{s—iy-'; {s—l)r"—sr"-'=—l. 



Ir—a 

 r—i 

 s—a 



log r 

 log /—log « 



« = : 



log (^— «;— log (5—/) 



^-/' 



« + (r — 1)>?_ _log [« + (r— i)^]— log « 

 r ' log r 



+ 1. 



log /— log [/r— (r— i)^] 



<2=/r— (r— 1)5; 71=-^ ^ "- ^ ^ +1. 



log r 



12. KxAMPi^KS AND Problems. 



1. Find the sum of 10 terms of the progression 3 + 9 

 H-27 + etc. 



2. Find the sum of 10 terms of the series To- + Tf"o+TATr> 

 etc., or the series .333 + 



j. Find the sum of 100 terms of the progression .3333+ etc. 

 ^. Sum 5 terms of the progression 27 + 270+2700, etc. 



5. Sum 10 terms of the progression 4—2 + 1— etc. 



6. Sum the series V3 + >/6 + vi2+ etc., to eight terms. 



7. Sum the series 3 — 2 + |— f+ etc., to nine terms. 

 S. Sum the series —4 + 8—16 + 32, etc., to 6 terms. 



p. The fourth term of a geometrical progression is 192 and 

 the seventh term is 12288 ; find the sum of the first three terms. 



