Summation

A summation, or sum, is the value of a number made of numbers using addition, e.g. 1 + 7 = 8.

Summation Notation
All sums can be represented with the symbol Σ, or sigma. E.g., the infinite series 1 + 1 +... can be represented like this:


 * $$\sum_{n=0}^{\infty\,}1^n.$$

The way summation notation works is as follows:


 * $$\sum_{x=m}^{n}f(x)$$

Here, m is the lowest value of the variable x, n is the highest value of the variable x, and f(x) is the equation used to find the values of the summation Σ. Therefore, m≤n in all situations.

Grandi's Series

 * Full article: Grandi's series

This series involves the problem 1 – 1 + 1 – 1 + 1 – 1 + 1... . This series was solved in 1703 by Italian mathematician, philosopher, and priest Guido Grandi, hence its namesake. It was found to be a divergent sum, meaning that it has no "true" value.

Grandi's series can also be represented as $$\sum_{x=0}^{\infty\,}(-1)^x.$$

e

 * Full article: e'''

The irrational constant e, which is approximately 2.718281828, can be represented with the following summation:


 * $$e = \sum_{k=0}^{\infty\,}\frac{1}{k!}\,$$