[ 2 9S 1 
XX. A hew Method of invejligating the Sums of Infinite Series . 
By the Rev. Samuel Vince, A. M. F. R. S. 
HE fummation of infinite feries is a fubjed, not only of 
curious {peculation, but alfo of the greateft importance 
in the various branches of mathematics and philofophy ; ia 
confequence of which it has always claimed a very confiderable 
fliare of attention from the moft: celebrated mathematicians, 
I (hail therefore make no apology for offering to the public 
the following new and very expeditious method, by which we 
may obtain the hums of a great variety of feries, moft of which 
have never before been treated of. As the fummation depends 
on the fums of the reciprocals of the powers of the natural 
numbers, tables of fuch fums are given as far as the 4°th 
power to twelve places of decimals, by which the fums of 
the feries will be found true to ten or eleven places ; and if 
greater accuracy were required (which is a cafe that can very 
rarely happen) it might eafily be obtained by continuing the 
tables. The firft and third columns (hew the fums, and ther 
fecond and fourth the powers correfponding* 
Read June 2, 1791. 
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