266 Theorems for the Summation of progressional Series. 
For the series 1+ hes +9xr3 2.2.5 (n?-+-n—2)a-", 
1+ 2v —m v =m 
.(e—2) +v%—nz (0 +3n)e 
v2 
Of 1+2a2-'+ 62-74 122-3.....(n?—n)x-™, 
2 —m —m 
a (e-2) + Quz¢v2—(Qn42+v(n2-+n)v 
v2 
Of 1 4+ 2a-'+62-7+ 1la-..... (nm? +3n—6)a-™, 
li (t—2) abt SME es = (x? + 5n—2)r 
Is SLA EE FT Megs re 
Of 14 20-'+ 72+ lda-3.... .(n?—2)0™, 
2x —m - = 
7 en) +1+4v2—(2n+ 1)e ™ ond + 2n—1)x 
v2 
Of a-'+6x-7-+ Ls are tae Sp says Gea re a ay 
4+v 
=n —n 
cn (r—z) ” —4(n+ })x  —v(2n? + 3n4+1)r 
oO e 
‘ v~ 
Of 14+52-'+102-7+ 16273... ee wee eon 
StS ern) n(o4 20) sah ” (n2+n)e 
v2 3 
Of 1+52-'+ 16x2°+433u-4.....(38n?—4n4 l)a-™, 
6 —m —m —m 
— («2—r) eee vi—r—(6n + 5)x ) —v(3n2 + 2n)x 
v 
2 s 
Of 1+-7a-' + 19a? 4.37273... 266 .(32?—3n+ 1)x-”, 
5+a2 —m 
oie =r a) By Sa—(62 + 3)" —v(Sn? +3n)r 
yp a 
Of 14 2a-'+ 91-7 + 240-3 45004 .... (m3 — m7) a7, 
Sr +22—1 
—m v —m 
(r—x7) +2274 73—0—(3n + a (3n2.+ 7n +2 +(n3 + In? +n)z) 
Of 14+7a-'+ 162-74 272-3 .....(m*+4n—5)a™, 
2 > —m —m —m 
—(x?—2) ” PUP 5r—(2n+7)x —v(n? + 6n)wx 
v 
v? 
Of 
