The addition of a sequence of numbers can be represented with the summation symbol (Σ).
Consider an addition sequence, S_{n}. Suppose the numbers to be added are u_{1}, u_{2}, u_{3}, …, u_{n}. We let
The sigma (Σ) symbol represents a summation of n components. As n increases without bound…
…we are led to consider a summation over infinite components, which is denoted by
Such an expression is called an infinite series. As an example, we can write the equation of state for a mixture of gases:
where P = total pressure | |
P_{i} = partial pressures of all i gas species | |
n_{i} = particle number per unit volume | |
k = Boltzmann’s constant, and | |
T = temperature |
This equation describes the total pressure P, as the summation of partial pressures P_{i}.
Study Astronomy Online at Swinburne University
All material is © Swinburne University of Technology except where indicated.