Theorems for the Summation of progressional Series. 267 
OF 14 22-"+ 101-*4. 302-3 + 68-4 .....(m3 + m)a-”, 
— (=e) ee vi—(6nx+v(3n2-++Sn)2” +0%(n3 +n)c) 
_—_—$—$<<— 
Of 1432-'+ 161-7 ++.452-73 ..... (3 —n*—n-+ l)am”, 
6+4v —m —7 = 
eee +23 — vr —(6n+6+ v(3n?+7n4+3)e "—v2(n3+2n2)2 
e 
vs 
Of 14 4a-" + 132-* 4261-3 ........ (2n? —n—2)a~”, 
4x = 
og (w—2) 4 1+v°—(4n+1)x ™ _—v(2n2 + 3n— De” 
v2 
Of 1+45a-'+4 13a-*4. 2525, 2... .(2n®—In-+4 1)a-™, 
4r —m —m -7 
4 (tr) + ur—4nx  v(2n?+ 2n+1)x 9 
ve 
Of 2" 4-39-4547 ooo. (2n—1)ax-", 
2Qnv Pass 2 fet 1) 
v+ : 
Of "+ 2-4 327, .....(na-"), 
2 +n 3 
vt 
Of a4a-™ 4 Oy e@eeevecse -(n*x-"), 
go 2: gm 
niv+ = —(2n—1)— = 
= V. - 
ve 
Of a" 43a""+46a7......4(n*-pn)a-", 
12" 
= (n’+n)+— —nr 
ve 
OF the series 2” + Sa-"4272~..... »(23x-"), 
n(n +1)?—3 Vi—(2n2-+-n)v°—3 + (3n—1)v 4-7" 4 97°” 
I Gada bu 7) a Sa 
Of 2” +907" +3607. ......(E(n?+n))2a-", 
3(n2+3n + 2)°—W—(n+1 »: 
v 
OF a7" +907" 42507 ......(2n—1)%a-', 
v!(2n-+1)2%—8(nv+-2)"e—vta "+ Br 
vs of 
ea 
