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XXV. A new Method of invefii gating the Sums of infinite Series. 
By the Rev. S. VINCE, A. M. of Cambridge, in a 
Letter to Henry Maty,. A. M. Secretary. 
Read June 6, 1782. 
s 1 R, 
H AVING lately dlfcovered fome very eaiy methods of 
inveftigating the fums of certain infinite feries, I have 
taken the liberty of requefting the favour of you to prefent 
them to the Royal Society. I have divided the fubjedl into 
three parts: the firfl: contains a new and general method of 
finding the fum of thofe feries which de moivre has found in 
one or two particular cafes ; but whofe method, although it be 
in appearance general, will, upon trial, be found to be abfo- 
lutely impracticable. The fecond contains the fummation of 
certain feries, the lafi: differences of whofe numerators become 
equal to nothing. The third contains obfervations on a cor - 
reft ion which is necefiary in inveftigating the fums of certain 
feries by colle&ing two terms into one, with its application to- 
a variety of cafes. 
I am,, &c. 
Cambridge, 
May 3, 1782. 
PART 
