of slowly converging and diverging Infinite Series, 353 



+ 1 



- -25 



+ • 140625 



- 97656 

 + 745768 



- 60562 



50889 

 43879 

 38565 

 34399 

 31045 

 54900 

 27450 

 •807175 



•807175 = sum of first six terms. 



7010 

 5314 

 4166 

 5354 

 8022 

 4011 



1696 

 1148 

 812 

 2023 

 1012 



548 

 336 

 654 



327 



212 

 106 



■834625 = inferior limit. 

 106 

 2* 



3 = 



834628 = superior limit. 

 .-. 834626 = S very nearly. 



A value which cannot differ from the truth by more than a 

 unit in the last decimal. It is, in fact, true in all its places, 



3. Let it be required to find the value of the diverging 

 series 1 2 3 4 „ 



-2778 

 2020 

 1515 

 3220 

 1610 



■758 

 505 

 884 

 442 



253 



126 



433625 

 -240476 



193149 = superior limit. 

 126 



•193145 = inferior limit. Hence 

 very nearly, which is true in the last decimal. 



Third Series, Vol.6. No. 35. May 1835. 



193147 = S 



2Z 



