44 EEV. T, P. KIEKMAI? ON MNEMONIC AIDS 



(F.) If «o Ui «a «8 ^ a^y function and its successive values, 

 fim up is t<o -f* Wi -j-t Wj -f- ?^3 + ... or junction up : up meana 

 with increasing subiiiclicea. 



fun oop is M -|" A w + A''*' -J- A'" "4" ••• 

 oop means + the successive diflferences : vid. n-bino, r-bin^ (7,a). 

 n-bino fun up is fun up with the co-efficients (1 -{- 1)", 

 n .71 — ' 1 



„ r.r — 1 _r.r — l.r — 2 



(GO A'M =: ± M + r.Ui + J 2 "2 + 2 2.3 "» i '" 



the upper signs to be taken when r is even, the lower when r is 

 odd, so that the series is repin, (7, c), the final term being 

 always positive. 



(H.) u.inc fid 't-adds, or 'le reci 'v-adds 



(« = « — 1, t) = « + 1 ; V. (7,a) (3,e) ) 



is u-or cip ii-adds ad fin. or ab in. 



(red := cip = ci, v.V). 



(The three ors correspond; i, c , the three antecedents go together, and 

 the three consequents.) 



This is the rule for summing factorials or differencing. Let 



P Pi Pi Pi -pu he an arithmetical series whose ewcrement or 



cjaliimon diffei'ence is i, 



^iX PiPiPa— Pu-i =:ppiP^...p^.i-\'C 



u£2, "-l — \ , I 



PPiP%-Pn PPiPi.'-pu-i^ 



The symbol 2 which is A"'> or reversed dtf, I call^<?.* I call 

 the factors adds ; being terms made by additions of the twcre- 

 ment »'. The first of the above equations has m-1 adds on the 

 left, and u adds on the right, terminating with the final one 

 (ad. Jin.) of those on the left : the second has m -|- 1 ndds on 

 the left, and u adds on the right, beginning from the first one on 

 the left (flb initio). Tlie constant is understood; and this 

 mnemonic for summation serves of course for differencing, if A"* 

 be transferred as A to the other side. 



"Want of space compels me to suppress all examples of mnemo- 

 nics on the Differential and Integral Calculus, on Equations, on 



