Semiformal Definition of a "Series":
A series
a_{n} is the indicated sum of all values of a_{n}
when n is set to each integer from a to b inclusive;
namely, the indicated sum of the values a_{a} + AA_{+1}
+ AA_{+2} + ... + a_{b1} + a_{b}.
Definition of the "Sum of the Series":
The "sum of the series" is the actual result when all
the terms of the series are summed.
Note the difference: "1 + 2 + 3" is an example of a
"series," but "6" is the actual "sum of the series."
Algebraic Definition:
a_{n} = AA_{} + AA_{+1} + AA_{+2} + ...
+ AB1_{} + AB_{}
Summation Arithmetic:
c a_{n}
= c a_{n}
(constant c)
a_{n}
+ b_{n}
= a_{n}
+ b_{n}
a_{n}
 b_{n}
= a_{n}
 b_{n}
Summation Identities on the Bounds:
b
a_{n}
n=a

c
+ a_{n}
n=b+1

c
= a_{n}
n = a

b
a_{n}
n=a

bc
= a_{n+c}
n=ac

b
a_{n}
n=a

b/c
= a_{nc}
n=a/c



(similar relations exist for subtraction and division as generalized
below for any operation g)
 
b
a_{n}
n=a

g(b)
= a_{g 1(c)}
n=g(a)

