170 A. USEFUL FORMULAS
A.5 SUMS AND FACTORIZATION RULES
FACTORIZATIONS OF POLYNOMIALS
• x
2
a
2
D .x a/.x C a/
• x
3
a
3
D .x a/.x
2
C ax Ca
2
/
• x
3
C a
3
D .x C a/.x
2
ax Ca
2
/
• x
n
a
n
D .x a/.x
n1
C ax
n2
C a
n2
x C a
n1
/
ALGEBRA OF SUMMATION
•
b
X
iDa
f .i/ C g.i/ D
b
X
iDa
f .i/ C
b
X
iDa
g.i/ •
b
X
iDa
c f .i / D c
b
X
iDa
f .i/
CLOSED SUMMATION FORMULAS
•
n
X
iD1
1 D n
•
n
X
iD1
i D
n.n C1/
2
•
n
X
iD1
i
2
D
n.n C1/.2n C 1/
6
•
n
X
iD1
i
3
D
n
2
.n C1/
2
4
A.5.1 GEOMETRIC SERIES
•
n
X
kD0
a
k
D
a
nC1
1
a 1
•
1
X
nD0
a
n
D
1
1 a
if jaj < 1
•
1
X
nD0
qa
n
D
q
1 a
if jaj < 1
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.