INFINITE SERIES. 53? 



PROBLEM IK 



f reduce a compound surd to an infinite series, 



RULE.* 



Extract the root ps in Arithmetic, and the operation, 

 continued as far as may be thought necessary, will give 

 the series required. 



EXAMPLES. 



}, Required the square root o^ a*-\-X^ in an infinite 

 series. 



*^ This rule is chiefly of use in extracting tiie square ropt ; the 

 operation being too tedious, when it is applied to the higher 

 powers. 



f Here the square root of the first term, a"^, is a, the first 

 term of the root, which, being squared and taken from the given 

 surd tf*4-*:^, leaves ** ) tliis remainder, divided by 2r?, twice 



tlic 



