PRELIMINARY % 
_ ie equations.—If “poo ape then Cardan’s wes gives 
vf Se 
oe “af beak ere oy +{-8 2 att) is 
The equation x + px* + gu +1=0 may be reduced to the form 
a A b=0 by substituting af for x in the given equation. 
‘The terms a, , (a+ 5), (a+ 2b), (a+ 3b), ete., are in arithmetical pro- 
on. The vn‘ term re the beginning is a+ (n - 1). 
r oo bhemglene 1}. 
_ If M, A, and N are in arithmetical progression, then anh, 
3 Ab the arithmetical mean of M and N. 
‘es a Geametrical progression. 
The terms a, ar, ar’, ar’, etc., are in tag progression, 
ES ~The n*™ term from the beginning i is ar"! 
4 a The sum of m term = “0” — 1)_a(l- my 
ee a: -l l- =f 
..@ If ris less than 1'the sum of an infinite number of terms is ics 
3 aM M, G, and N are in geometrical progression, then G= ./MN, and 
the geometrical mean of M and N. 
Saeco Ss, =sum of n terms. 
8, =14+243+. - tn=5(n+1). 
2 (n+ 1)(2n + 1) 
6 
8, = 124+ 224+ 37+. o'te.-e. + 
>. . | 
a foam TP 4: SP es --* . oy tnte (MOE DY 
& Binomial Hessese (a+a)"= 
“f Se enertes Gantt ME) ee) 
, a 
(n-2) . . (n-r+l) | 
: 1 
‘he @ 1) term of (a+z)"= ae=)) G uae f 
Aeoe jr, read factorial r,=1.2.3....... 7% 
hase 5) and logarithmic series. 
At? A®x? Atz 
with ied Bod se 
2 Pikes A=log,a, and e = base of Napierian von” of logarithms, 
rs he, e= 271828. . . 
ne : hat +0)=2- matt, a 
