JNFIKTE SERIES. 327 



EXAMPLES. 



I. Reduce to an infinite series. 



I X 



'^ answer. 



Here it i§ easy to see how tHe succeeding terms of the 

 quotient may be obtained without any further division. 

 This law of the series being discovered, the series may be 

 continued to any required extent by the appHcation of it. 



I ^ . . . 



2. Reduce to an infinite series. 



1 4-^ 



-i_ ~ i—x+x'—x^+x"^-^, &c. 



the answer. 



Here the exponent of x also increases continually by i 

 from the second term of the quotient j but the signs of 

 the terms are alternately -j- and — . 



3. Reduce 



