484 ON THE SUMMATION OF SERIES, 
This series will be found very convenient in 
ealculating the hyperbolic logarithm of #, when 
x is pretty large, and when y differs from # only 
by unity. 
Cor. If the difference between w and y be 
unity, the difference of their logarithms will be 
Leal 1 ] l 1 
expressed by s(> +—-)-33(4-- +s ) nearly, 
which is exceedingly near the truth, if x be a 
large number. 
Ex. 3.—Required the sum of terms of the 
n 
series whose general term is (m+av) . 
Here, we have f (~) =(m+azr) ; {s (xv)dx 
n+l 1 n—1l iil 
=(m+ar) ; f(2)=an (m+az) _,f (a)= 
a (n+1) 
3 n— v a 
a.n (n—1) (n—2).(m+az) ft (2)=an 
nm—5 
(n-1),...(2—4).(m+ar) &c., &c., &e. 
By substituting these values in equation (15), 
and the values of A, B, C, &c., as previously 
determined, we shall have 
