Math2.org Math Tables: Series Properties |
(Math) |
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} = a_{a} + a_{a+1} + a_{a+2} + ... + a_{b-1} + a_{b}
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 |
| | (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) |