|Dave's Math Tables: Series Properties|
|(Math | Calculus | Expansions | Series | Properties)|
Semi-Formal Definition of a "Series":
A series an is the indicated sum of all values of an when n is set to each integer from a to b inclusive; namely, the indicated sum of the values aa + aa+1 + aa+2 + ... + ab-1 + ab.
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."
an = aa + aa+1 + aa+2 + ... + ab-1 + ab
c an = c an (constant c)
an + bn = an + bn
an - bn = an - bn
Summation Identities on the Bounds:
n = a
(similar relations exist for subtraction and division as generalized below for any operation g)
= ag -1(c)