33 2 ALGEBRA. 



2. Requirednhe square root of a*— ^* in an infinite 



series. 



Ans. O' 





3. Convert -i/ i-}-! into an infinite series. 



4. Let V^— a;* be converted into an infinite series. 



i J, 1 Z 



Ans ^_— — ^— i^~-^ &c. 

 2 8 16 128' 



5. Let y/i — *v^ be converted into an infinite series. 



Ans. i—j — ^— g-, &c, 

 SIMPLE 



ihe first term of the root, gives — for the second term of the 



2fl 



root, which, added to 2a, gives 2^-| for the first com- 



X* 



pound divisor, which being multiplied by — > and the product «* 



2a 



x^ . . x^ 



J taken from the first remainder w*, there remains 1 



4«^ 4a 



this remainder, divided by 2«, gives — —-- for the third term of 



die root, which must be added to the double of (z-^ , the tv/o 



2a 



first terms of the root, for the next compound divisor. And by 

 proceeding thus, the scries may be continued as far as is desired. 



Note. In order to have a true series, the greatest term of 

 the prpposed surd must be always placed first. 



