THEOKY OF THE PARTITIONS OF NUMBERS. 



55 



Further simplification of this series cannot he effected because each term of the 

 sum must be considered on its merits and does or does not add to the numerical 

 result as may appear. 



Art. 142. Writing the result for even order 2n 



it appears that the result for uneven order 2i+l may be written 



For the squares of simple orders we have the results 

 ORDER 2. 



ORDER 4. 



1= 1 



Z= 

 



ORDER 5. 



12345 



II 



s 



