How to solve double summations?

Hi everyone!

Can anyone tell me how to solve problems of double summation?

What are tricks to solve them? For instance how to solve this problem:

$\sum_{ω=1}^{\infty}\sum_{n=1}^{\infty}\frac{ω^{2}n}{3^{n}(n(3^{ω})+ω(3^{n}))}$ Also help with generalised methods .

2 years, 6 months ago

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Not every double sum has a closed form, just as not every single summation has a closed form. Many summation solutions are ad hoc.

- 2 years, 6 months ago

What is ad hoc? Can you explain me general properties to solve double summation using an example?

- 2 years, 6 months ago

"Ad hoc" is a term used to describe methods/solutions that are non-generalizable and applicable to a particular case.

- 2 years, 6 months ago