- #1
feryee
- 9
- 0
what is the result for the following double summation:
##\sum\limits_{i \neq j}^{\infty}\alpha^i\alpha^j ##
where ## i, j =0,1,2,...##
##\sum\limits_{i \neq j}^{\infty}\alpha^i\alpha^j ##
where ## i, j =0,1,2,...##
Well actually i have the final result but simply i couldn't get the same answer using geometric sum. Here is the final result:micromass said:Express it as an iterated sum and then apply the result for a sum of a geometric series. What do you get?
A double summation is a mathematical operation where two summations are performed consecutively. This means that the sum of the first sequence is calculated, and then the sum of the resulting sequence is calculated.
This notation represents the product of two variables, \alpha^i and \alpha^j, raised to the power of i and j respectively. In other words, it is equivalent to \alpha^{i+j}.
The result of a double summation is calculated by first evaluating the inner summation, which results in a single value. This value is then used as the variable in the outer summation, which ultimately produces the final result.
Double summation is commonly used in various fields of science, such as mathematics, physics, and statistics. It is used to simplify and solve equations involving two variables, and it also has applications in discrete mathematics and calculus.
Yes, there are other types of summation, such as single summation, which involves only one sequence, and multiple summation, which involves more than two sequences. There are also various methods and formulas for calculating summations, depending on the specific scenario and application.