378 



Trans. Acad. Sci. of St. Louis. 



TABLE IV. 



some integral number, the value of x n may be represented 

 by either of the systems above described. For example 

 of re = 25 and n==2 and the first term of the series be 

 taken as unity, the final term will be 



Z = 2X25 2 — 1 = 49. 



The sum of the series will be 625. The number of terms 

 will be 25. The sum of the series is equal to the square 

 of the number of terms, as is shown in Eq. (3). 



If the second method above discussed be adopted, equa- 

 tions (4) give as the first and last terms 



a = 25 2 — 25 % + l = 121 



J 

 Z = 25 2 + 25^ — 1 = 129 



The number of terms will then be 



2—1 



tf = 25 2 = 5. 



