ON THE 
SUMMATION OF SERIES, 
AND ON 
DEFINITE INTEGRATION. 
BSYoROUBERT “RAW SON: 
(Read November 12th, 1844.) 
The summation of # terms of a series, in func- 
tions of 2, is a proposition, which involves in its 
solution a considerable portion of the difficulties 
that are to be met with in the science of pure 
mathematics. Nor, indeed, is this much to be 
woudered at, when we consider, that, nearly all 
the obstacles, which oppose the progress of the 
investigator, in the application of Analysis to the 
Physical sciences, may be reduced, finally, to this 
single proposition. 
Mathematicians have not been, hitherto, suc- 
cessful in the investigation of a general formula, 
